Anyone who says they don’t care more about themselves than they do about others is lying or else mentally ill. Anyone who says they don’t care more about their own children than other people’s children is lying or else a bad parent. We are biologically programmed to be selfish and to help those who share our DNA. We are also biologically programmed to distrust faces which are different from the faces we see every day. Anyone who denies these facts is denying well-established science.
In the political and social sphere, we should encourage equality of opportunity in competition precisely because that leads to better outcomes for everyone in an economic system: win-win.