Paul Edwards documented some objections to reincarnation:
Edwards catalogues common sense objections which have been made against reincarnation . . .
Nothing to be afraid of, there clearly is no reincarnation. Once your dead your dead. People on this forum will not accept this, but this is what science says. Anything else is magical thinking.
I have no idea whether or not reincarnation really happens but most of these objections are pretty poor.
"1) How does a soul exist between bodies?" This just seems to be a question about how non-physical things can exist altogether. The question is almost non-sensical if the only explanations one accepts are physical ones, and if one accepts non-physical explanations then there are myriad of possible answers.
"2) Tertullian's objection: If there is reincarnation, why are not babies born with the mental abilities of adults?" This is a fairly obvious question, along the lines of question 5: "If there is reincarnation, then why do so few, if any people, remember past lives?" I am pretty sure that people who believe in reincarnation have not failed to notice that most babies don't remember their past lives or have their past abilities. Rather they believe that when a soul is reincarnated its past memories are repressed. Those that do remember past lives are those that have managed to overcome the repression just like people who repress memories can later recover them or be trained to circumvent the repression.
"3) Reincarnation claims an infinite series of prior incarnations. Evolution teaches that there was a time when humans did not yet exist. So reincarnation is inconsistent with modern science." This is silly because it is based on a false premise that "Reincarnation" (as it was an entity!?) claims to be infinite. I have never seen such a claim made by reincarnation believers. Second, even if reincarnations did claim to be an infinite series, there are certainly scientific theories that postulate the existence of multiple universes in a series or parallel to each other that can stretch back infinitely. There is no reason to believe that those other universes do not have sentient life.
"4) If there is reincarnation, then what is happening when the population increases?" See above, just because reincarnation exists doesn't mean that everyone born is reincarnated. If you do not believe in an infinite series, then everyone has to have a first time in this world. If you do believe in an infinite series, the populations of the inenumerable other universes will suffice to supply souls to our universe.
5) See above
6) "They assume that when a human dies, before he is reincarnated, he exists as an astral body invisible, completely undetectable by scientific instruments, yet somehow able to travel at a very high speed and penetrate material objects like walls, roofs, and human bodies. He can travel and see things even though deprived of a brain and eyes and means of locomotion."
This seems to just be a rehash of the earlier objection that cannot fathom the existence of non-physical things. Non-physical things, not bound by physical laws, would not have the limitations that your imagining souls to have.
7) "After a period of time, one's astral body picks out or is thrown into a woman's body at the moment of conception. Even though the person may have been very old and knowledgeable at death, when reborn he has a new, different baby's body and none of his memories. Yet he is somehow the same person."
This too is a rehash of previous objections that essentially amount to "reincarnation cannot be true because I find the concept weird."
8) "To account for the great increase in population, it must be assumed that many souls incarnated on this earth did not live on it previously. They must somehow have migrated from some other planets or dimensions or god knows what. Finally, most people must have done bad in past lives because they will enter the wombs of mothers in poor, over-populated countries where their lives are likely to be miserable."
At least this acknowledges that the "infinite reincarnation" question is not really much of a question. This also appears to assume that reincarnation is a means of reward and punishment. But even if reincarnation were a means of reward and punishment, I think it is very likely true that most people would have done at least some bad things in past lives that would warrant some sort of "atonement" in their next life, maybe in the form of growing up in poverty.
Frankly the content of these questions, unless they were made in jest, reflects very poorly on their author.