Christ forbade swearing by God, or at all:
Matthew 5:34-37
34 But I say unto you, Swear not at all; neither by heaven; for it is God's throne:
35 Nor by the earth; for it is his footstool: neither by Jerusalem; for it is the city of the great King.
36 Neither shalt thou swear by thy head, because thou canst not make one hair white or black.
37 But let your communication be, Yea, yea; Nay, nay: for whatsoever is more than these cometh of evil.
Above, the Lord says that if you ever have to say more than "yes" or "no", there is something wrong with that situation. This is also reiterated explicitly in James 5:12.
However, over and over again, Muhammad explicitly taught to swear oaths, and that we are to swear by Allah:
Surah 24:6-9
6 And those who accuse their wives ˹of adultery˺ but have no witness except themselves, the accuser must testify, swearing four times by Allah that he is telling the truth,
7 and a fifth oath that Allah may condemn him if he is lying.
8 For her to be spared the punishment, she must swear four times by Allah that he is telling a lie,
9 and a fifth oath that Allah may be displeased with her if he is telling the truth.
Sahih al-Bukhari 7401
Narrated Ibn `Umar:
The Prophet (ﷺ) said, "Do not swear by your fathers; and whoever wants to swear should swear by Allah."
This is reiterated in Surah 5:89, 5:106-107, 16:91, Sahih al-Bukhari 2679, 6108, 6646, and Sahih Muslim 1646d, 1646f. Muhammad and his companions swear by Allah hundreds and hundreds of times in the Hadith. Modern Muslims also use the phrase "Wallahi" - some quite frequently - which means "I swear by Allah".
So, Christ taught not to swear at all, then Muhammad shows up, and institutionalizes not only swearing, but the most egregious form of swearing by God, completely contradicting Christ.
When giving us the model of prayer, Jesus begins with the words "Our Father":
Matthew 6:9
9 After this manner therefore pray ye: Our Father which art in heaven, Hallowed be thy name.
This is repeated in Luke 11:2. The fact that believers are children of God is a major theme in the New Testament (Matthew 7:11, John 1:12, Galatians 3:26, 4:4-6: 1 John 5:1, etc.), as is the fact that Jesus is the Son of God (John 3:16, Matthew 8:29, Mark 1:1, Luke 1:35, etc.).
In contrast, Muhammad entirely rejected the concept of God being a father to anyone:
Surah 19:88-92
88 They say, “The Most Compassionate has offspring.”
89 You have certainly made an outrageous claim,
90 by which the heavens are about to burst, the earth to split apart, and the mountains to crumble to pieces
91 in protest of attributing children to the Most Compassionate.
92 It does not befit ˹the majesty of˺ the Most Compassionate to have children.
Surah 37:151-52
151 Indeed, it is one of their ˹outrageous˺ fabrications to say,
152 “Allah has children.” They are simply liars.
This teaching is reiterated in Surah 2:116, 5:18, 17:111, 19:35, 21:26, 23:91, 39:4, 43:81, and 72:3.
Jesus, just as the Old Testament prophets (Genesis 6:1-4, Exodus 4:22, Deuteronomy 14:1, 32:5: 2 Samuel 7:14, Job 1:6, 2:1, 38:7, Psalm 2:7, 2:12, 73:15, 89:26, Isaiah 43:6, 63:16, 64:8, Hosea 1:10), taught a God that was a Father, with human beings as His children. He did so dozens of times, and taught us to open our prayers with that fact. Muhammad decried the entire concept of God as father.
In the Bible, Jesus teaches very clearly that if you marry someone who is divorced for any other reason than fornication, you have committed adultery:
Matthew 5:31-32
31 It hath been said, Whosoever shall put away his wife, let him give her a writing of divorcement:
32 But I say unto you, That whosoever shall put away his wife, saving for the cause of fornication, causeth her to commit adultery: and whosoever shall marry her that is divorced committeth adultery.
This is in reference to the single provision that God gave in the Law for divorce, which was an immediate annulling of the marriage because of fornication (Deuteronomy 22:13-21, 24:1-4), and it is reiterated in Matthew 19:3-9, Mark 10:2-12, and Luke 16:18.
Muhammad not only taught that marrying a divorced person was permissible (Surah 2:230), he also personally married a divorced woman, whom his own stepson Zaid had divorced because of Muhammad, as covered in this article:
Surah 33:37
37 And ˹remember, O Prophet,˺ when you said to the one for whom Allah has done a favour and you ˹too˺ have done a favour, “Keep your wife and fear Allah,” while concealing within yourself what Allah was going to reveal. And ˹so˺ you were considering the people, whereas Allah was more worthy of your consideration. So when Zaid totally lost interest in ˹keeping˺ his wife, We gave her to you in marriage, so that there would be no blame on the believers for marrying the ex-wives of their adopted sons after their divorce. And Allah’s command is totally binding.
Moreover, in a bizarre verse, which actually contains the words of Umar (Sahih al-Bukhari 402), he threatens his wives with divorce, and then intimates that he might remarry women who have been divorced:
Surah 66:5
5 Perhaps, if he were to divorce you ˹all˺, his Lord would replace you with better wives who are submissive ˹to Allah˺, faithful ˹to Him˺, devout, repentant, dedicated to worship and fasting—previously married or virgins.
So, Jesus says that remarriage after divorce is strictly forbidden, Muhammad teaches the opposite, and then personally breaks Christ's commandment to marry Zaynab.
Jesus taught that in Heaven, there will be no marriage:
Mark 12:23-25
23 In the resurrection therefore, when they shall rise, whose wife shall she be of them? for the seven had her to wife.
24 And Jesus answering said unto them, Do ye not therefore err, because ye know not the scriptures, neither the power of God?
25 For when they shall rise from the dead, they neither marry, nor are given in marriage; but are as the angels which are in heaven.
This is found in the parallel accounts in Matthew 22:30, and Luke 20:35.
In contrast, Muhammad taught that believers will be married to women in Heaven, and have intercourse with them for all eternity:
Surah 2:25
25 Give good news ˹O Prophet˺ to those who believe and do good that they will have Gardens under which rivers flow. Whenever provided with fruit, they will say, “This is what we were given before,” for they will be served fruit that looks similar ˹but tastes different˺. They will have pure spouses, and they will be there forever.
This is reiterated in Surah 3:15, 4:57, 36:55-56, 37:48-49, 38:52, 43:70-71, 44:54, 52:20, 55:56, 55:70-74, 56:22-23, 56:35-37, and 78:33. These wives are also mentioned in Sahih al-Bukhari 2796, 3254, 3327, 4879-80, Sahih Muslim 2834a, 2834c, 2834e, Sunan ibn-Majah 4333, and Jami at-Tirmidhi 1663, 2522, 2536, 2735.
Muhammad's entire concept of Heaven is completely different from the one in Christianity, and even Judaism. The Bible describes the eternal state as dwelling with God in a totally remade earth (Isaiah 65:17-25: 1 Corinthians 15:20-28, Revelation 21:1-4), not Muhammad's heavenly brothel, which is apparently inside of a 60 mile-wide pearl (Sahih al-Bukhari 3243, 4879-80, Sahih Muslim 2838a-c, Jami at-Tirmidhi 2528). In creating a heavenly paradise of his own perverted desire, he again contradicted what Christ taught.
In the Sermon on the Mount, Christ forbade vain, repetitious prayer:
Matthew 6:7-8
7 But when ye pray, use not vain repetitions, as the heathen do: for they think that they shall be heard for their much speaking.
8 Be not ye therefore like unto them: for your Father knoweth what things ye have need of, before ye ask him.
However, Muhammad taught his followers to do what is the definition of a vain repetition:
Sahih Muslim 597a
Abu Huraira reported Allah's Messenger (ﷺ) as saying:
If anyone extols Allah after every prayer thirty-three times, and praises Allah thirty-three times, and declares His Greatness thirty-three times, ninety-nine times in all, and says to complete a hundred:" There is no god but Allah, having no partner with Him, to Him belongs sovereignty and to Him is praise due, and He is Potent over everything," his sins will be forgiven even If these are as abundant as the foam of the sea.
This is also narrated in Sahih al-Bukhari 843, 3705, 5361-62, 6318, and Sahih Muslim 595a, 596a, 597b, 2727a, 2728a-b.
In some of these narrations, he recommended one do this before bed, but in others, as highlighted above, he recommended it after every prayer. That would amount to 500 vain repetitions per day.
Elsewhere, he taught the chanting of a yet another phrase 100 times per day:
Sahih al-Bukhari 6405
Narrated Abu Huraira:
Allah's Messenger (ﷺ) said, "Whoever says, 'Subhan Allah wa bihamdihi,' one hundred times a day, will be forgiven all his sins even if they were as much as the foam of the sea.
This is also narrated in Sahih Muslim 2691, and Jami at-Tirmidhi 3468.
Of course, everyone on earth who does vain repetitions, when called out for doing so, will immediately scream that whatever they are doing isn't vain repitition. This is immaterial. If chanting 3 prayers 33 times each, potentially multiple times per day, isn't vain repitition, and if chanting a single phrase 100 times per day isn't vain repitition, nothing is. Muslims, God is not going to hear you just because you speak more. That's what Jesus Christ taught, and Muhammad contradicted.
Returning again to the Sermon on the Mount, notice Christ's teaching on the topics of prayer, giving, and fasting:
Matthew 6:1-8, 16-18
1 Take heed that ye do not your alms before men, to be seen of them: otherwise ye have no reward of your Father which is in heaven.
2 Therefore when thou doest thine alms, do not sound a trumpet before thee, as the hypocrites do in the synagogues and in the streets, that they may have glory of men. Verily I say unto you, They have their reward.
3 But when thou doest alms, let not thy left hand know what thy right hand doeth:
4 That thine alms may be in secret: and thy Father which seeth in secret himself shall reward thee openly.
5 And when thou prayest, thou shalt not be as the hypocrites are: for they love to pray standing in the synagogues and in the corners of the streets, that they may be seen of men. Verily I say unto you, They have their reward.
6 But thou, when thou prayest, enter into thy closet, and when thou hast shut thy door, pray to thy Father which is in secret; and thy Father which seeth in secret shall reward thee openly.
7 But when ye pray, use not vain repetitions, as the heathen do: for they think that they shall be heard for their much speaking.
8 Be not ye therefore like unto them: for your Father knoweth what things ye have need of, before ye ask him.
16 Moreover when ye fast, be not, as the hypocrites, of a sad countenance: for they disfigure their faces, that they may appear unto men to fast. Verily I say unto you, They have their reward.
17 But thou, when thou fastest, anoint thine head, and wash thy face;
18 That thou appear not unto men to fast, but unto thy Father which is in secret: and thy Father, which seeth in secret, shall reward thee openly.
What is the constant thread running through these teachings? The command to perform your good deeds privately.
In contrast, we can look at the practices of Muslims, as taught to them by Muhammad:
Muhammad's religion teaches the exact type of outward, hypocritical, vain religiosity that Christ hated. Also, since precisely none of these things are ever required of believers by God in the New Testament, Muhammad squarely falls under the condemnation of the following:
Mark 7:6-7
6 He answered and said unto them, Well hath Esaias prophesied of you hypocrites, as it is written, This people honoureth me with their lips, but their heart is far from me.
7 Howbeit in vain do they worship me, teaching for doctrines the commandments of men.
In the Gospels, Jesus is frequently worshipped (Matthew 2:11, 8:2, 9:18, 15:25, 20:20, 28:9, 28:17, Mark 5:6, Luke 24:52, John 9:38).
For instance:
Matthew 14:33
33 Then they that were in the ship came and worshipped him, saying, Of a truth thou art the Son of God.
He also taught that worship is due only to God (Matthew 4:10, Luke 4:8). Yet, never once does Jesus rebuke anyone for worshipping Him.
If you, as a human being, are being worshipped, you have an obligation to correct the person, and tell them to stop. We see exactly this in an account of one of Jesus's disciples, Peter:
Acts 10:25-26
25 And as Peter was coming in, Cornelius met him, and fell down at his feet, and worshipped him.
26 But Peter took him up, saying, Stand up; I myself also am a man.
In the book of Revelation, when John worships at the feet of an angel, the angel likewise tells him to stop:
Revelation 19:10
10 And I fell at his feet to worship him. And he said unto me, See thou do it not: I am thy fellowservant, and of thy brethren that have the testimony of Jesus: worship God: for the testimony of Jesus is the spirit of prophecy.
Therefore, we see that Peter made the right choice, and even when John mistakenly worships an angel, the angel corrects him. Jesus Christ, who was sinless (John 8:46: 2 Corinthians 5:21, Hebrews 4:15: 1 Peter 2:21-22: 1 John 3:5), and always made the right choice, did no such thing, ever.
In contrast, what we see in the Quran is a rebuke to those who worship Jesus Christ:
Surah 5:116
116 And ˹on Judgment Day˺ Allah will say, “O Jesus, son of Mary! Did you ever ask the people to worship you and your mother as gods besides Allah?” He will answer, “Glory be to You! How could I ever say what I had no right to say? If I had said such a thing, you would have certainly known it. You know what is ˹hidden˺ within me, but I do not know what is within You. Indeed, You ˹alone˺ are the Knower of all unseen.
Surah 9:30-31
30 The Jews say, “Ezra is the son of Allah,” while the Christians say, “The Messiah is the son of Allah.” Such are their baseless assertions, only parroting the words of earlier disbelievers. May Allah condemn them! How can they be deluded ˹from the truth˺?
31 They have taken their rabbis and monks as well as the Messiah, son of Mary, as lords besides Allah, even though they were commanded to worship none but One God. There is no god ˹worthy of worship˺ except Him. Glorified is He above what they associate ˹with Him˺!
Muhammad taught that Jesus was just a man, and repudiated worship. The real Jesus accepted worship, and never rebuked anyone for worshipping Him.
In the Quran, Muhammad repudiated the Christian claims that only believers in Christ will be saved:
Surah 2:111
111 The Jews and Christians each claim that none will enter Paradise except those of their own faith. These are their desires. Reply, ˹O Prophet,˺ “Show ˹me˺ your proof if what you say is true.”
In response to the above challenge to "Show me your proof if what you say is true" - allegedly given by the same God who wrote the Gospel (Surah 5:46-47, 5:66, 5:68, 5:110, etc.), we offer the following explicit proof:
John 3:36
36 He that believeth on the Son hath everlasting life: and he that believeth not the Son shall not see life; but the wrath of God abideth on him.
Other exclusivist statements in Scripture include John 3:18, 8:24, 14:6, Mark 16:16, Acts 4:12 and 1 John 5:12. You wanted proof? There's the proof.
As can be clearly seen, Muhammad directly castigates Jesus Christ himself, in this Quran verse. Jesus said He was the only way, and Muhammad, in so many words, calls Him a liar.
Then, in the Hadith, he steals the role of sole mediator (1 Timothy 2:5) from Jesus, and assigns it to himself (Sahih al-Bukhari 4476, 4712, 6565, 7410, 7440, 7510, and Sahih Muslim 193a-e, 194a), even though he was a sinner (Surah 40:55, 47:19, 48:1-2, Sahih al-Bukhari 6307). He not only denies Christ, but then tries to steal His glory.
Muhammad taught that when you are attacked, you are to respond in kind:
Surah 2:194
194 The sacred month for the sacred month; and sacrilege calls for retaliation. Whoever commits aggression against you, retaliate against him in the same measure as he has committed against you. And be conscious of God, and know that God is with the righteous.
Notice what Muhammad did not say. He did not say "defend yourself". He said "retaliate against him in the same measure as he has committed against you". That's taking vengeance. If you argue otherwise, don't claim in the next breath that Allah or Muhammad are the best of communicators, because you've just improved on the Quran. The option to retaliate in-kind is also given in Surah 16:126.
In contrast, Jesus Christ taught not to take vengeance for ourselves when others wrong us:
Matthew 5:38-45
38 Ye have heard that it hath been said, An eye for an eye, and a tooth for a tooth:
39 But I say unto you, That ye resist not evil: but whosoever shall smite thee on thy right cheek, turn to him the other also.
40 And if any man will sue thee at the law, and take away thy coat, let him have thy cloak also.
41 And whosoever shall compel thee to go a mile, go with him twain.
42 Give to him that asketh thee, and from him that would borrow of thee turn not thou away.
43 Ye have heard that it hath been said, Thou shalt love thy neighbour, and hate thine enemy.
44 But I say unto you, Love your enemies, bless them that curse you, do good to them that hate you, and pray for them which despitefully use you, and persecute you;
45 That ye may be the children of your Father which is in heaven: for he maketh his sun to rise on the evil and on the good, and sendeth rain on the just and on the unjust.
Also see Luke 6:27-36, and Romans 12:19. What a contrast. Show me anything like the above in the Quran, or the Hadith. The beauty, mercy, and holiness of the teachings of Christ is obvious, and obviously superior to Muhammad's.
Jesus taught many things about himself that Muhammad completely rejected, including:
The Bible - which is the only record that anyone has for the life of Jesus - teaches an entirely different Jesus to the one Muhammad invented. According to the testimony that Jesus Christ gave about himself, He is far more than a mere prophet, and certainly not secondary to the sinner (Surah 40:55, 47:19, 48:1-2, Sahih al-Bukhari 6307) Muhammad.
Islam does affirm Jesus. It's a Jesus that has never existed anywhere, and completely contradicts the only Jesus that history or Christians have ever known. But, any religion can affirm that Jesus, because he is entirely invented out of thin air, in order to suit the needs of the liar trying to hijack Him.