Not so, actually.
I'll grant you that they're self-centered and many fall prey to greed as fall prey to gluttony, sloth, anger, vengeance ... all manner of human faults.
But a society that is MORAL and in which all men are essentially equal, retain sovereignty over themselves and their families, enjoy the fruits of their labor and are able to purchase and retain their own private property usually turns out very selfless folks.
The United States still is very much this way ... if only because the folks in the "red" portion of the Bush/Gore election map still more than make up for the entirely atomistic, selfish, adolescents of the left and the middle.
I refuse to believe it is human nature to be greedy. We are social by nature and -- be it a matter of faith or pure logic -- even some of my atheist friends live such that they treat others always as they themselves wish to be treated.
Only those CONDITIONED by an immoral or pseudo-moral system like capitalism would believe all humans are naturally greedy by nature.