I believed reincarnation was probable when I first read about it in the 1970s, but after a few years I came to regard it as improbable. I think the matter should continue to be studied scientifically to try to determine for certain what is true about the spirit world, but my reasons for doubting reincarnation are as follows.
(1) The idea of reincarnation originated from ancient myths in which people mistook the planets for gods, because plasma phenomena in space and sometimes in atmospheres gave some of the planets a human-like appearance, so Saturn, which was close to Earth in ancient times, appeared to be the first god and appeared to create other gods as planets in the sky, then ate some of his own children, then was killed by one of his children, Zeus/Jupiter, who became the new supreme god, whom the ancients thought was the reincarnation of Saturn. Mars then seemed to replace Jupiter as the supreme god and was considered the reincarnation of Jupiter. Here's a good video that shows some of the main findings from comparative mythology: https://www.youtube.com/watch?v=t7EAlTcZFwY.
(2) It would not be humane for God or nature to force people to reincarnate against their will. People should be able to learn lessons in the spirit world just as easily as in the physical.
(3) Since there are more people every year, many of the people would have new spirits that never existed before, unless one person could reincarnate in several bodies. There's no reason to assume that infants don't have spirits in the womb or at conception. It may be that physical life cannot form without a spirit "seed", "soul", or "germ", and that the physical body grows because the spirit body grows first, or simultaneously. So science needs to study this to see if physical life can exist without spirit life. If it cannot, then when a spirit thinks it's reincarnating in a baby's body, it may just be forcing the baby's new spirit out of its own body and the possessing spirit would then be stealing a body that doesn't belong to it. When children, or even adults, think they remember a past life, they may just be sensing the memories of a spirit who lived a physical life and who is probably near them, as with telepathy. Science may be able to determine what is the truth. Even if the science of physical people is not able to do that by itself, it may be able to with the help of science by spirit persons. People in spirit should be able to conduct science as easily as we do. In fact, science may have come from the spirit world.
The human race or the whole biosphere may have a collective consciousness which some people are able to tap into and describe partially. Authors of ancient sacred literature, or bibles, may have done that. If the collective consciousness is like a supercomputer, it may explain some of the seemingly miraculous aspects of some bibles. The super-consciousness may have the ability to predict the future, which some psychics could tap into and write into bibles. There is some evidence that the Jewish, Christian and Muslim bibles have some supercomputer-like patterns within them. I don't know if other bibles were studied to see if they also have similar patterns.
If there is a super-consciousness, it may have known that ancient myths have a strong subconscious influence on humans, so the ancient myth of the sacrificial king may have been used in order to influence humanity's subconscious to replace fear and hatred with Love for all, as Jesus and the Apostles apparently tried to explain. The Bible says Jesus is an example for all, so the crucifixion seems to have been meant to show people the power or Love over fear. If Jesus rose from the dead, it encouraged people to follow Jesus' example. The Muslim Bible says Jesus did not suffer on the cross, so, if that's true, then God was not cruel to him.
I only got interested in the Bible in the late 1990s, but I came across several sources that helped me make some sense out of it. One was an 1895 book, called The Encyclopedia of Biblical Spiritualism, which showed that the Bible is full of phenomena known to spiritualists, like communicating with the dead and other paranormal things. Ivan Panin showed in the early 1900s that the Bible seems to have the supernatural patterns that I mentioned. Messianic Jews showed online that some important things in the Bible were misinterpreted by later Christians starting 300 years after Jesus' time under Constantine. And now Universalist Christians are showing that the Bible does not claim that Hell is eternal or that anyone will not be tortured forever. At least one early Christian writer said Buddhism was a good friend of Christianity. The change from a physical body to a spirit body can also be considered as reincarnation. So can the transformation from a low spirit body to a higher spirit body. Reincarnating in physical bodies over and over and losing one's memory each time, is like going to first grade and learning it well, then forgetting everything and going through first grade again and repeating that over and over.