I do appreciate your substantive response, and the copious thought you have given the matter.
I disagree with many of the cultural assumptions you make regarding both species of hominids, and therefore with your conclusions. The evidence shows that H. sapiens and H. neanderthalensis cohabited for tens of thousands of years in Europe, and this shows that simple animosity wasn't the sole interaction between them.
If it had been, the newcomers would have been eradicated instantly, while we were few in number and vulnerable. Neanderthals conducted the first burials, with flowers heaped on the dead, and without eating them first. I do not doubt that cannibalism occurred, but you cannot deny H. sapiens has also done the same thing.
Also, we aren't prey. I was raised wild, on an island in Alaska, and we are the dominant predators, even without firearms - except when faced with the ire of a protective mother. Three beasts have caused me to undoubtedly make the right decision to run away, and the mother bear, the mother moose, and my ex were the only things I ever feared enough to flee in total panic.
Every other bear, mountain lion, elk, wolf, and even predators in the sea, I ran across fled from me, and with good reason. Not so long ago I read of a drunken young man staggering home in Alaska at 2am, crossing a bridge, and alarming a mother Grizzly fattening on the salmon below.
He beat her to death with a stick when she attacked him. I have seen Grizzly bite through a steel tool box full of tools, mangling the wrenches and ratchets within like baling wire, and never even chipping a tooth. I damn near pissed myself. But the guy whose pickup bed the bear had sought a tasty snack in, opened the door to the truck and began to get out, and the bear ran, watching over his shoulder to see if the man 1/4 his size was gonna chase him down and kill him.
We are the dominant predator, and have been since we evolved - through stability processes. Read Eugene McCarthy, and you will either be enlightened, or outraged.
Either way, stability theory better explains the origin of species than neo-Darwinian theory, and Neanderthals were human, not beasts.
"The evidence shows that H. sapiens and H. neanderthalensis cohabited for tens of thousands of years in Europe"
Probably not:
http://www.bearfabrique.org/Catastrophism/wiealt.html
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I see that you are consulting sources, which is a great way to get information. It is important to consult as many sources as possible, and to consider how they get their information, so that one can reasonably assess the reliability of that information.
I have been unable to find other sources that have pulled this particular number out of their posterior orifice, and suggest you replace it from whence it came.
I, in short, do not find the evidence presented in the link you provided compelling, and the technique he used to arrive at his conclusion is best described as 'completely making it up'.
Rather than ignoring all other sources of information and settling for the one that is least convincing, I do suggest you seek out more sources, at least if you want to be able to make arguments that have the potential to convince me of anything other than your ignorance.