Apparently it is said that around AD 553, the early christian church leaders eliminated doctrines from the Bible that showed proof of reincarnation. Some suggest that the doctrines stayed the same and where never tampered with.
Now in the Bible there are some statements that have double meaning or could suggest reincarnation:
"John 3,3" No one can see the kingdom of God unless he is born again.
"James 3,6" The wheel of nature.
"Galatians 6,7" A man reaps what he sows.
"Revelation 13,10" If anyone is to go into captivity, into captivity he will go. If anyone is to be killed with the sword, with the sword he will be killed.
Christians argue that reincarnation is a threat towards the whole essence of christianity, the need for Christ's redemptive sacrifice for our sins becomes useless if man is to keep being reborn and we are paying the consequence of our sins and attaining salvation ourselves in further lives. In other words it is believed then that Christ would have died for nothing.
Now I believe in Jesus and was brought up a Christian but I don't rule out the idea of reincarnation. For me I don't see reincarnation as an excuse to take advantage of sin because I will get to be reborn as others may see it. I just believe that it could take more than one lifetime to keep learning and ascending to a higher spiritual level. I don't believe Christ died for nothing, he did teach us lessons. It is said by Christians that we will all be judged at the end of time but why not keep coming back to make that improvement if you feel you really need to, or get that second chance that may have been abruptly taken away from you eg. "a small child dying unexpectedly". That just makes better sense to me than just sitting in limbo until the end of time waiting to be judged/punished. Is that what God really wants for us - punishment, or does he want us to learn and ascend higher spiritually, I mean he gives us free will choices while we are alive, wouldn't he also do that if we were on the other side? These are just my opinions.
What do others think of this topic, be interesting to read about it.