The first way in which Pope Benedict XVI (1927-2022 AD) disproves the Papacy is his view on Protestantism, and how it utterly contradicts the historical Catholic Church's teaching.
The Council of Trent (1545-1563 AD) was called in response to the Protestant Reformation, and explicitly anathematized dozens of Protestant beliefs, and those who held them. Similarly, prior Popes lamented over the mere existence of Protestantism, declared it unambiguously heretical, and made unity with the Bishop of Rome an absolute requirement for Salvation:
Pope Pius XI - Rerum Omnium Perturbationem (1923 AD)
4 Like those brilliant examples of Christian perfection and wisdom to whom We have just referred, he seemed to have been sent especially by God to contend against the heresies begotten by the Reformation. It is in these heresies that we discover the beginnings of that apostasy of mankind from the Church, the sad and disastrous effects of which are deplored, even to the present hour, by every fair mind.
Pope Pius XI - Mortalium Animos (1928 AD)
11 Furthermore, in this one Church of Christ no man can be or remain who does not accept, recognize and obey the authority and supremacy of Peter and his legitimate successors. Did not the ancestors of those who are now entangled in the errors of Photius and the reformers, obey the Bishop of Rome, the chief shepherd of souls? ... Let them hear Lactantius crying out: "The Catholic Church is alone in keeping the true worship. This is the fount of truth, this the house of Faith, this the temple of God: if any man enter not here, or if any man go forth from it, he is a stranger to the hope of life and salvation. Let none delude himself with obstinate wrangling. For life and salvation are here concerned, which will be lost and entirely destroyed, unless their interests are carefully and assiduously kept in mind."
However, Pope Benedict XVI - who wrote many books - says the following:
Pope Benedict XVI - Principles of Catholic Theology, pg 202
It means that the Catholic does not insist on the dissolution of the Protestant confessions and the demolishing of their churches but hopes, rather, that they will be strengthened in their confessions and in their ecclesial reality.
Pope Benedict XVI - The Meaning of Christian Brotherhood
The difficulty in the way of giving an answer is a profound one. Ultimately it is due to the fact that there is no appropriate category in Catholic thought for the phenomenon of Protestantism today (one could say the same of the relationship to the separated churches of the East). It is obvious that the old category of "heresy" is no longer of any value.
Heresy, for Scripture and the early Church, includes the idea of a personal decision against the unity of the Church, and heresy's characteristic is pertinancia, the obstinacy of him who persists in his own private way. This, however, cannot be regarded as an appropriate description of the spiritual situation of the Protestant Christian.
In the course of a now centuries-old history, Protestantism has made an important contribution to the realization of Christian faith, fulfilling a positive function in the development of the Christian message, and above all, often giving rise to a sincere and profound faith in the individual non-Catholic Christian, whose separation from the Catholic affirmation has nothing to do with the pertinancia characteristic of heresy. The conclusion is inescapable, then: Protestantism today is something different from heresy in the traditional sense, a phenomenon whose true theological place has not yet been determined.
Above, he explicitly says that Protestantism does not need to be dissolved, and also that Protestants are not heretics. Rather, the phenomenon of Protestantism is unprecedented, and cannot be classified.
Of course, this is nonsense. There have always been dissenters, and the Church has always been explicit in their condemnation. He even tries to lump in Eastern Orthodoxy into this unclassified group, which is historically laughable. A major belief of the Orthodox is a rejection of the Filioque clause in the Nicene Creed. Yet, all who rejected the Filioque were explicitly anathematized in the Council of Florence (1445 AD). The Church's historical position on both Protestants and Orthodox is very clear. Prior Popes and councils unambiguously condemned them as heretics, and anathematized them dozens of times.
He also desires to see Protestants "strengthened in their confessions and in their ecclesial reality". That is, strengthened in their unanimously anathematized, heretical confessions, and their false ecclesiology. From a historical Catholic perspective, this is heretical, and hateful.
The Roman Catholic view of Tradition is that it is absolutely binding, and constitutes part of the deposit of faith, just as the Scriptures:
Second Council of Nicaea (787 AD)
If anyone rejects any written or unwritten tradition of the church, let him be anathema.
However, Benedict XVI admitted that Catholicism has absorbed "much human pseudotradition", and as a result, is partially culpable for "the general crisis of tradition that afflicts mankind":
Pope Benedict XVI - Principles of Catholic Theology, pg 100
The Church is tradition, the concrete situs of the tradition of Jesus, into which - let us admit it - much human pseudotradition has found its way; so much so, in fact, that even, and even precisely, the Church has contributed to the general crisis of tradition that afflicts mankind.
This admission - while honest and obvious - is heretical from a Catholic perspective. If a Protestant said the above, they would be swiftly and loudly rebuffed by Catholic apologists. Yet, the Pope - who knows more about tradition than either of us - admits that much of the Medieval tradition that is practiced by Roman Catholics is invalid. Amen. Good man. But, bad for a Roman Catholic. Such scandalous things must not be said.
The third way in which Pope Benedict XVI disproves the Papacy is his departure from traditional Catholic doctrine regarding the Jews.
Historically, the Roman Catholic Church has taught that all Jews will go to Hell, and anyone practicing the Old Testament Law, including keeping the Sabbath, will go to Hell:
Council of Florence (1445 AD)
It firmly believes, professes and teaches that the legal prescriptions of the old Testament or the Mosaic law, which are divided into ceremonies, holy sacrifices and sacraments, because they were instituted to signify something in the future, although they were adequate for the divine cult of that age, once our lord Jesus Christ who was signified by them had come, came to an end and the sacraments of the new Testament had their beginning. But it asserts that after the promulgation of the gospel they cannot be observed without loss of eternal salvation... Therefore it denounces all who after that time observe circumcision, the sabbath and other legal prescriptions as strangers to the faith of Christ and unable to share in eternal salvation, unless they recoil at some time from these errors.
It firmly believes, professes, and proclaims that those not living within the Catholic Church, not only pagans, but also Jews and heretics and schismatics cannot become participants in eternal life, but will depart "into everlasting fire which was prepared for the devil and his angels" (Matt. 25:41), unless before the end of life the same have been added to the flock;
Notice that the above specifically says that the Church "denounces all who after that time observe the sabbath", referring to the beginning of the New Covenant.
However, Pope Benedict XVI extolled Jews for their Sabbath keeping:
Pope Benedict XVI - Address to the Jewish Community (September 12, 2008 AD)
Dear friends, it is with great pleasure that I meet with you this evening. Our meeting auspiciously coincides with the vigil of the weekly celebration of the shabbat, the day which from time immemorial has occupied a significant position in the religious and cultural life of the people of Israel. Every pious Jew sanctifies the shabbat with the reading of the Scriptures and the reciting of the Psalms. Dear friends, as you know, the prayer of Jesus also was nourished by the Psalms. Regularly he went to the temple and the synagogue. There he too listened to the word on the Sabbath. There he wanted to underline the goodness with which God cares for man, even in the arrangement of time. Does not the Talmud Yoma (85b) say: the Sabbath is offered to you, but you are not offered to the Sabbath? Christ has asked the people of the Covenant to recognize always the unprecedented greatness and love of the Creator for all humanity. Dear friends, because of that which unites us and that which separates us, we share a relationship that should be strengthened and lived. And we know that these fraternal bonds constitute a continual invitation to know and to respect one another better.
The above is dishonest. It's dishonest to dialogue with Jews fraternally, and affirm their practices on the Sabbath, when you are aware that an infallible ecumenical council of your Church has specifically anathematized them all to Hell, and condemned all those who keep the Sabbath.
The fourth way in which Pope Benedict XVI disproves the Papacy is his heretical view on Islam.
His first error is in stating clearly that Muslims worship the same God as Christians - an error introduced in Vatican 2, as covered in this article:
Pope Benedict XVI - General Audience (August 24, 2005 AD)
This year is also the 40th anniversary of the conciliar Declaration Nostra Aetate, which has ushered in a new season of dialogue and spiritual solidarity between Jews and Christians, as well as esteem for the other great religious traditions. Islam occupies a special place among them. Its followers worship the same God and willingly refer to the Patriarch Abraham.
Pope Benedict XVI - Address in Jordan (May 9, 2009 AD)
Muslims worship God, the Creator of Heaven and Earth, who has spoken to humanity. And as believers in the one God we know that human reason is itself God’s gift and that it soars to its highest plane when suffused with the light of God’s truth.
Muslims do not worship God. They worship an idol (1 Chronicles 16:26), who is a demon (1 Corinthians 10:20). The Quran says that God has no son (Surah 19:88-92), and that all Christians are going to Hell (Surah 3:85, 5:72). The Bible says that a Muslim, as any non-Christian:
Similarly, Pope Benedict XVI stated multiple times that he has respect for Islam, and esteem for Muslims:
Pope Benedict XVI - Christmas Address (December 22, 2006 AD)
My Visit to Turkey afforded me the opportunity to show also publicly my respect for the Islamic Religion, a respect, moreover, which the Second Vatican Council (cf. Declaration Nostra Aetate, n. 3) pointed out to us as an attitude that is only right.
Pope Benedict XVI - Address to Turkish Ambassador (January 19, 2007 AD)
During my memorable Visit, I frequently expressed the respect of the Catholic Church for Islam and the esteem of the Pope and the faithful for Muslim believers, especially during my Visit to Istanbul's Blue Mosque.
To use an Old Testament comparison, this is declaring respect for Baal worship, and esteem for the followers of Baal. It is heretical to give respect to a Satanic, false religion of the worst sort. Likewise, any esteem for Muslims has to be clarified to be totally disconnected from their Islamic identity - or rather, completely in spite of it.
There is nothing whatsoever to esteem or respect in Islam. It teaches its followers that any who embrace the Lord Jesus Christ and converts to Christianity from amongst them must be killed (Sahih al-Bukhari 3017, 6922, Sahih Muslim 1676a-d, etc.). It is entirely Satanic, its preachers are apostles of Satan, and its followers are all deceived, and living a life of sin in the name of a false religion. Saying anything even remotely positive about Islam is an act of hatred for those trapped in it, as you are only appealing to their misgiven suppositions - for instance, that they worship God - rather than truly loving them, which would be to tell them the truth about how their religion is false, they are under the wrath of God because they worship Satan, and their religion is leading them to damnation.
Pope Benedict XVI made repeated, heretical statements, which contradicted both the Bible, and traditional Roman Catholicism.
Not a single word of the above was ever retracted. Yet, Catholicism teaches that every Pope is "the true Vicar of Christ, the head of the whole church, and the father and teacher of all Christians" (Council of Florence, 1439 AD), and "religious submission of mind and will must be shown in a special way to the authentic magisterium of the Roman Pontiff, even when he is not speaking ex cathedra" (Vatican 2, Lumen Gentium, 1965 AD). These statements of Benedict XVI prove this doctrine to be heretical, and false.
Benedict XVI was a false prophet, who, while not as ecumenical as his successor Francis, was well within the post-Vatican 2 school of utter apostasy, both to Christianity, and historical Catholicism.