I have no problems rejecting reincarnation. Why is that a problem? Most Christians and I'd probably stretch to say all Jews reject it as well. Reincarnation (as a hinduistic idea) means in this life I can be rewarded or punished for what I did in a previous life. Which means if the lessons I learned in the last life through life itself were wrong, then there is no hope for me ascending toward something better. I'm not entirely sure how the Buddhist system is handled. But as a mathmatics minded person. The idea of reincarnation without new creation, doesn't add up, also it doesn't explain things like extinction. If that animal/creature was a step in the reincarnation cycle, how could you justify extinction of a species?