Arguably humans cooperate even more than they compete. Examples of cooperation are easy to find throughout nature. So is parasitism, but humans generally find that loathsome as a human activity.

The argument from nature is a fallacy. Just because something is doesn't mean it ought to be.

> it's the one that best matches the reality of nature (competition)

This doesn't seem right: it doesn't match the history of reality, in which capitalism has repeatedly stymied rather than fostered competition.