Exactly. The current theory, I believe, is that humans didn't "exterminate" Neanderthals, we just out bred them. This might be due to differences in "character". I can't reproduce the argument here, and I don't have a link, so I'm being a bit vague but the point is, something in the Human mental make up caused us to form more successful communities than the Neanderthals. The several Hominins running around Europe in the past seem to have coexisted for some time, and interacted enough that some interbreeding took place. Over time, Neanderthal faded away, leaving only the bits of DNA we got from them.