The reason why Neanderthal man died out was because Homo Sapiens discovered marriage before they did. There, I have said it, and you have read it here FIRST.
I believe that for PC reasons that the division of labour hypothesis was ignored because it would inevitably lead to awkward questions being asked about feminism, which it would be HERESY to question.
Why Neanderthal Man died out is explained at http://thevoiceofreason-ann.blogspot.com/2010/11/why-neanderthals-died-out.html
Neanderthal man lived in a matriarchy (a society that condones female promiscuity eg feminism) while Homo Sapiens lived in a patriarchy (a society that condones male promiscuity and supports the institution of Marriage).
The feminist doctrine of gender equality inevitably makes it promote the idea that women have the right to be as promiscuous as men, ignoring the fact that it is women who get pregnant and are the ones left holding the baby and expected to look after their babies. Now feminist orthodoxy (which is Communistic in nature and application) decrees that taxpayers (who are mostly male) are to bail out these Slut Single Mums who have fucked up their lives. Eventually, this will drag everyone else down to their slut and bastard level.
Indeed, Slut Single Women who have fucked up their lives are currently being glamorised.
Mary F Pols, who allowed a penniless and jobless loser to impregnate her in ACCIDENTALLY ON PURPOSE wrote a book http://www.amazon.co.uk/Accidentally-Purpose-one-night-unplanned-pregnancy/dp/0141038403/ref=sr_1_1?ie=UTF8&qid=1328012408&sr=8-1 which is now a US sitcom http://www.cbs.com/primetime/accidentally_on_purpose/. You gotta hand it to the Americans for having the knack of making depravity wholesome. Another example is COUGAR TOWN. http://en.wikipedia.org/wiki/Cougar_Town
It would not be fair to call Neanderthal women "sluts" because a matriarchy - as the Neanderthal society must have been because they had not yet discovered the institution of marriage - would not be familiar with the concepts of sluttery AKA fornication AKA adultery precisely they operated a kind of sexual communism or a free for all fuck fest that we in the West would be all too familiar with.
Patriarchal Homo Sapiens who created the institution of Marriage had men who would take more of an interest in their offspring, stay with the women who bore their children thereby producing progressively better offspring that also retained the culture of their ancestors. (This made them culturally more sophisticated as well as facilitating social cohesion.) The patriarchs operated a kind of sexual meritocracy and efficient labour division between male and female roles, which would have been the beginning of Eugenics (an ideology that concerns itself with improving or at the very least maintaining the quality of the generation for that society), while Neanderthal man became progressively more degenerate. In the end, they died out after the matriarchy (who were slut and bastard people) was easily defeated by the patriarchy (who respected the institution of marriage).
There are lessons to be learnt from this by the slut and bastard governments of the 21st century West, I would have thought, but they are probably too slut and bastard to listen to reason now.