We wouldn't have survived to become the species we are now if those were our "natural" traits. We're socal creatures, we live in communities. If anything, we are now living in the least compatible societal arrangement for our species. There is evidence that even neanderthals would care for the their eldery and dead.

Greed, in my opinion is a "modern" notion designed to propagandize and misdirect away from the true culprit of our time, and that is motive. Specifically, profit motive. Greed, much like laziness, is a made up notion by the capitalist class. It implies that you can be altruistic and "fair" with your capitalistic desires, and anyone who isn't doing as such is simply morally bankrupt.

It allows people to ascribe a personal moral failing to the capitalist, instead of analyzing the underlying motivations and structures that govern their behavior. It means people can, as temporarily embarrassed millionaires, imagine that they would never make that kind of moral failing given the opportunity.

Except, they would make that same "mistake" if they were ever given the opportunity, because capitalism demands it.