2 Samuel 24:1
1 And again the anger of the Lord was kindled against Israel, and he moved David against them to say, Go, number Israel and Judah.
1 Chronicles 21:1
1 And Satan stood up against Israel, and provoked David to number Israel.
The first account says God moved David to "number the people", the second says that Satan provoked David to "number the people". Therefore, the alleged contradiction is that the Bible says God is actually Satan, or something to that effect.
A bigger question - why does God allow the Devil to exist at all?
The Devil only exists to carry out God's justice and serve God's purposes. If a Christian is disobedient, they are delivered to Satan (1 Corinthians 5:5) who is eager to destroy humanity. If someone rejects God, then Satan is given free-reign to blind that person and use them as he pleases.
That's the only reason why God allows this being who has cultivated an extreme hatred for Him and His creation to exist. Satan is a pawn that God uses to carry out justice and give people what they deserve.
Satan accuses humanity to God (Job chapters 1-2), which is why he's called the "adversary" (1 Timothy 5:14-15: 1 Peter 5:8). If they are in violation, Satan is sometimes turned loose on them. Such is the situation that God has set up.
So now that we understand the dynamic between God and Satan, it can be said that God moved David to number the people by turning Satan loose on him to reveal the pride in David's heart. Satan then provoked David to actually do the act, and David, due to his greed, complied.
Also note the statement in James chapter 1:
James 1:13-14
13 Let no man say when he is tempted, I am tempted of God: for God cannot be tempted with evil, neither tempteth he any man:
14 But every man is tempted, when he is drawn away of his own lust, and enticed.
We see more of the dynamic between temptation, God, us, the Devil, and where the culpability lies. It's from within our own wicked hearts that sin arises:
Mark 7:21-23
21 For from within, out of the heart of men, proceed evil thoughts, adulteries, fornications, murders,
22 Thefts, covetousness, wickedness, deceit, lasciviousness, an evil eye, blasphemy, pride, foolishness:
23 All these evil things come from within, and defile the man.
The greed was already in David's heart. God used the Devil to put that greed on display. God did not cause the greed, neither did the Devil. God did not tempt David to sin, the sin was already in David, and the Devil's temptation was simply for David to manifest it.
If David had not completed that sin by acting on his sinful desire, it wouldn't have been as bad of a sin. In the same way, lusting after a married woman, according to Christ, is technically adultery (Matthew 5:28), though physically going and doing it, obviously, is far worse.
If God didn't use Satan, then He would just use someone else to carry out His justice on earth or move haters of Him or those who would like to do wrong to blindness and evil. Again, Satan is just an arbitrary pawn who is in a situation that God has set up to parse those who truly love Him from those who don't.
God is interested in getting to the deepest desires of His creation and separating a group for Himself that pleases Him. That's the whole purpose of this planet. Satan plays a role in that operation, as can clearly be seen by these two verses. His role is to act as a means of punishment, and as a "garbage collector", as it were.
None of His decisions are flippant or arbitrary. The situation that He set up is the best possible way to accomplish what He wants with humanity - laying bare the deeds and desires of beings which He has given total free will to either love or reject Him.