Even the Bible doesn't dismiss reincarnation as a possibility.
Yes it does.
Hebrews 9:27
Just as man is destined to die once, and after that to face judgment,
28 so Christ was sacrificed once to take away the sins of many people; and he will appear a second time, not to bear sin, but to bring salvation to those who are waiting for him.
Then take your pick. Either that Bible verse (attributed to the Apostle Paul) is wrong, or Jesus was a liar when he did some of his disciples that they would not taste death before he returned with his new kingdom. (Matthew 24:34 says "Truly I saw to you, this generation will not pass away before these things take place." Matthew 16:28 says "Assuredly, I say to you, there are some standing here who shall not taste death till they see the Son of Man coming in His Kingdom.") Or perhaps what God defines as death is totally different than how we define it, which would make sense given that God knows what happens after we leave our physical bodies.
But if I really want to get on your nerves, I can nitpick the Bible all day.
Lets discuss the last words of Jesus. According to Mark 15:34, Jesus last words were "My God, my God, why hast thou forsaken me?" Matthew 27:46 agrees with this, and in Matthew 27:50, it adds that he then cried out in a loud voice and breathed his last. Luke 23:46 says that his last words were "Father, into your hands I commit my spirit. But John 19:30 says that the last words of Jesus were simply "It is finished." There is no way for all of those be literally correct.
We can also examine Mark 16. The earliest manuscripts of Mark 16 end at verse 8, where it describes the women (including Mary Magdalene) who had seen Jesus risen from the dead trembling with fear, and telling not a soul because they were afraid. However, a few verses later (note that these verses did not appear on the earliest manuscripts) have Mary Magdalene then going and telling the disciples who were mourning their master that he had risen. The probability is that one of the people copying down Mark 16 to spread the word found the chapter ending at verse 8 to be unsatisfactory, so he added onto it.
It's possible to be a Christian. It's not possible to take every single verse of the Bible as literal, because it contradicts itself many times.
