Okay, so there are X billion people on the planet today. So all these X billion people, if they're reincarnated, came from someone who used to be before they were born. But there were fewer and fewer people as you go back in time, back to Adam and Eve who were the only two.
So see? it doesn't work.
Unless there're extraterrestrial life forms. But then what's killing them off by the billions? Why can't they be reborn where they died? Did their planet blow up in a horrible explosion, killing everybody?
Do people who remember previous lifetimes remember being green and living on Mars-- or being whatever color and living on whatever other planet? They never do, do they. So see? Reincarnation doesn't make sense.
I'm not sure why I just remembered that.
Now since then, I've grown to consider reincarnation differently. Perhaps there's a GARGANTUAN clump of Soul out there in the other world- a lump that the soul of you, and me, and George W. Bush and everyone else ever to be has been scraped out of. Like a bunch of sillyputty in the can. So Christopher Columbus dies- his soul gets kneaded back into the lump of soul-stuff, a little smarter, a little more experienced- and his soul's experience is commingled with that of the whole lump. Later, another lump of soul is extracted- and perhaps this one remembers being Christopher Columbus.
I can believe that, but I still can't believe in 'strict' reincarnation. hrmn.