For a long time, the many anecdotal stories of reincarnation aroused my interest.
Separately, as I read the Bible, the occasional passages suggesting cases of past lives aroused my interest even more.
For example, the words of Matt 17:10-13 explicitly stated that John the Baptist was Elijah. The disciples interpreted it this way, and I interpreted the verses this way too.
Furthermore, the Bible did not explicitly state that there is no such thing as reincarnation.
Please refer to the article "Reincarnation in the Bible" in http://reluctant-messenger.com/reincarnation-bible-verses.htm
This article appeals to me because it gives samples of many parts of the Bible that suggest the phenomenon of reincarnation. It's explanation tallies with my own logical conclusion relating to Matt 17: 10-12, Matt 24:34, Job 1:20-21, and other verses. Jesus replied, "To be sure, Elijah comes and will restore all things. But I tell you, Elijah has already come, and they did not recognize him, but have done to him everything they wished. In the same way the Son of Man is going to suffer at their hands." Then the disciples understood that he was talking to them about John the Baptist." (Matthew 17:13)
Why the Catholic church threw out the doctrine of reincarnation in the earlier years (AD 553, The Second Council of Constantinople?), and why most other churches subsequently adopted the same idea, I don't know.
Little did I know some other writers also observed this anomaly too; and in their studies, concluded that reincarnation may be is a 'lost doctrine' in most Christian churches.
I finally reasoned out why the prophets in the old testament talked to the people about prophecies that would be fulfilled in hundreds and thousands of years down the road. (I mean, why would my generation bother if someone predicts the world would split into 2 halves in 20,000 years time? Long long time after my generation is gone.) Such prophecies are meaningless unless this same generation would be there, in another incarnation, at the time the prophecies are fulfilled.
It appears possible that souls could be reincarnated until such time when they accept Jesus Christ as Saviour and Redeemer. And upon that acceptance, they no longer need to be reincarnated again. Perhaps you have other conclusions, but do read the article quoted above.
"...For I know whom I have believed and I am convinced that He is able to guard what I have entrusted to Him until that day." 2 Tim 1:12