Why did Saint Cyril murder Hypatia and burn the library of Alexandria? Did he do this for God? Did he kill anyone who didn’t believe in God and burn everything that have nothing to do with the belief in God?
Almost certainly Cyril did not murder Hypatia. Carl Sagen wrote a speculative and not particularly scholarly account of Hypatia. He was quite biased against Christianity, which might partially explain his unsubstantiated speculations. More careful scholars have mentioned ancient accounts in which the female neo-Platonic philosopher and mathematician Hypatia was killed by a "Christian" mob in Alexandria. Whether this is what happened is hard to say for sure, but given the antiquity of the claim, it is reasonable to give credence to this claim. According to the account, Hypatia was killed by this mob because of her pagan beliefs and the fact she was a very influential philosopher. Let us, for a moment, assume that this is a true story. If so, then this would be a shameful and completely unacceptable act for Christians to commit. Jesus said that we should love our enemies and pray for them. There is no conceivable way to justify such a violent act by a Christian on anyone, whether their philosophy disagrees with Christianity or not. It is a regrettable fact that people who take the name Christian have committed heinous acts, including the destruction of cultural treasures which were associated with pagan ideas and even taking the life of pagans simply for not believing in God. In any case, there is no evidence that Cyril was responsible for Hypatia’s death.
It is almost certainly not true that Cyril killed Hypatia, and it is even more unlikely that he had anything to do with the destruction of the library in Alexandria. I do not know where you got this idea, but perhaps this came from the unscholarly Sagan version of her life. The question of the burning of the library in Alexandria is quite controversial. It is not even certain that the library was burned in the fourth century at all. The library was destroyed during the reign of Aurelian (AD 270-275) when he retook the city after a rebellion. Also, the emperor Theodosian ordered the destruction of many pagan temples and other institutions in AD 395, which led to the destruction of a library which may have contained some of the books originally in the famous Alexandria Library. The historian Socrates Scholasticus mentions what happened in Alexandria at this time, but he makes no mention of the destruction of the Alexandrine Library. In any case, it is almost certainly a spurious claim that Cyral had anything to do with the burning of this human treasure, even if we grant that the library was burned during his life. I was able to find no reputable evidence that he was connected to the destruction of the library.