“Neanderthal DNA is generally described as being about halfway between ours and that of a chimpanzee.”
Did you even bother to read the rest of the article? After examining 12,000 protein gene sequences in 50 living humans and one Neanderthal, they found only 88 differences and speculate that with 500 living humans and some other Neanderthal samples the differences might approach zero. The number of differences for chimps was far, far greater. Furthermore, in 50 years of following anthropology studies and discoveries, and taking some courses as well, I have NEVER heard that Neanderthal were halfway between us and chimps.
I've read LOTS of articles on the subject. All indicate that Neanderthal DNA was halfway between ours and that of an ape; that we could no more interbreed with Neanderthals than we could with goats or horses; that we are therefore not in any way descended from Neanderthals and are unrelated to them.
There is the further consideration which should be obvious but which evolutionites refuse to consider which is that all other hominids were further removed from us THAN the neanderthal and that, if we couldn't be desdended from the Neanderthal, then we could not be descended from any of the others either.
If you wanted to go on thinking we were descended from hominids, you would have to produce some new hominid, closer to us in both time and morphology THAN the neanderthal, and the works and remains of that guy would be all over the map and very easy to find had he ever existed.
The Neanderthal was basically a very advanced, extinct ape, the most advanced member of the same family of creatures as chimpanzees and gorillas. We are another and separate family of creatures.