It's interesting isn't it - some people appear to feel threatened either way.
I don't wholeheartedly believe in reincarnation (or anything else 'woo' like ghosts and spirits and psychics etc) but I do get into debates with people who rubbish it with science. Or worse, scientific 'facts'. Which is different from them just believing something else (I have no problem with that).
Mostly because it's something we currently do not have the ability to perceive.
What evidence has shown us however, is that it’s highly highly unlikely to happen and I know where I’d place my billion dollars bet!
The strength of an analogy is in the similarities though.
What you mean by evidence is that we've agreed upon an accepted reality that humans don't spontaneously turn into cats. That's because we have eyes (to see) or cameras (to record) human behaviour over thousands of years and have never observed a human turn into a cat or the effects of a human turning into a cat. Or any other animal from which we could draw conclusions.
Nobody and nothing has ever been able to observe the state of death or the effects of death (in terns of a spirit / soul / consciousness). You can't use the same no observation over thousands of years acceptance of reality because a method for observation doesn't exist.
So the analogy is flawed. A slightly less flawed analogy would work better if the human claimed he could only turn into a cat when nobody or nothing was around to observe him. Did he?
But now that's a philosophical question similar to the tree falling in the deserted forest making a sound. Science can attempt to answer it but... it's still a philosophical question.
And I don't necessarily think this is a bad thing. I remember reading something once about physics along the lines of some things thought to be accepted will turn out to be wrong, but if we're really lucky then most of it will be wrong. Because isn't that the joy in it? The unknown.