Reply to Avatar
You said, "Modern humans maybe weren't yet "formed" then, but when they did, Neanderthals couldn't compete with them." There is no evidence that modern humans and Neanderthals ever "competed." Even if they did, it was on a very localized scale (i.e. Neanderthals were extremely widely distributed relative to modern humans).
If (and this is a big if) Neanderthals "perished," I suspect it was due to an epidemic, no evidence here though. It has been suggested that Neanderthals are NOT extinct, and exist among us today, that in fact we ARE part Neanderthal. I suspect that this is true.