Suppose it's true, as this article suggests, that egalitarianism is natural. Nothing of a normative nature follows. Aggression is natural. Tribalism is natural. Rape is natural. Are we to conclude that these are acceptable, much less required? And haven't we been told by scientists and philosophers that the fact that theism comes naturally to human beings has no bearing on the truth of theism? Then why should the fact that egalitarianism comes naturally to human beings have a bearing on the truth of egalitarianism? No cherry picking, please. Either everything natural is, as such, acceptable or nothing natural is (on that account) acceptable.
Addendum: Notice the conflation of egalitarianism and fairness. There is no necessary connection between these concepts, as anyone who has read the fable of the ant and the grasshopper knows. An equal distribution of goods between a deserving person and an undeserving person is unfair, not fair. An unequal distribution of goods between people differing in desert, in which goods are proportioned to desert, is fair, not unfair.