Well, reincarnation doesn’t actually make logical sense, when you think about it.
Now, if you reject the Church’s teaching that human souls are unique and want to put all souls on the same level, whether you are talking ants, dogs or humans, than you need to explain why people come back as one animal versus another. For example, if you want to say people can come back as dogs, why not cockroaches? Logically, they would come back as either. If you believe that, you need to set up a system that determines who gets to be a dog and who gets to be a cockroach. Eastern religions will give you an answer, but that involves worshiping many gods, a caste system and abandoning Jesus and Christianity altogether.
If, on the other hand, you accept the Catholic Church’s teachings that human souls are unique, then we must be reincarnated only as human beings. So, if we’re just talking about human souls reincarnating into future human beings, there is absolutely no logical way that would work because of the increase in the number of human beings on the planet. New Age types would claim that some people are ‘old souls’ and some are new. Does that make sense based on what we know about God? Would he give only some of us a ‘second chance’ to live another life in a different time? Do we account for our sins only in the life where we lived more holy, or does He average our behavior during both lifetimes? What if we were Christian in one life and atheists in the second life? Which would determine our fate, the first or the second?
We can’t believe in something simply because we like the idea. This temptation is very real and attempts to put us on equal ground with God. That is a very unfortunate trap. It would be much better to rely on what Jesus told us will happen when we die. Personally, I’d prefer one round here on earth, do my best, and then join God in heaven (if I can make it there).