Once again, the basic non-evolution of modern man, you seem to have missed it. The Neanderthal was a very advanced, extinct ape; his DNA was almost exactly halfway between ours and that of a chimpanzee. That rules the Neanderthal out as a plausible ancestor for modern man (via any process involving or resembling evolution at least) and, since all other hominids were clearly further removed from us THAN the Neanderthal, that rules them all out. There is nothing on this planet which we could be descended from via evolution.
Why be willfully ignorant?
You state that Neanderthal DNA was halfway between ours and chimps, which means we had a common ancestor, not that we descended from neaderthals or chimps.
Besides, Neaderthals created art, hunted, and made fire. Does that sound like an advanced ape to you?