It seems to me that human nature (and the survival of species) are comprised of both - competition in order to ensure survival and cooperation for the same purpose. If any society were to be entirely one or the other it would likely become extinct. And the species that knows best how to use competition (not individual but as a species) to survive would do so to defend against threats of other SPECIES (not humans).
However, since we are the dominant species on the planet, we wind up competing against ourselves by creating false divisions - black vs white, gay vs straight, male vs female, country A vs country B, etc.
So the question in my mind is, are we not at a stage of evolution that should favor cooperation over competition?

"The liberals can understand everything but people who don't understand them."
Lenny Bruce

"The cleverest of all, in my opinion, is the man who calls himself a fool at least once a month."
Dostoevsky