In a patriarchal dominance hierarchy, if you don't win, you lose. It's entirely zero-sum and it never occurs to them to even try for win-win. Therefore, every interaction is a contest for dominance, and you can never be close to anyone because they are all your competition. No wonder they are always on the verge of melting down - that outlook is terrible for the mental and emotional health of members of a highly social species who were the only hominids to survive, largely because they were the friendliest and most cooperative of the bunch.
Also, among primates, there is only one alpha male and one alpha female - not an entire class of alphas - and the alpha male has to campaign hard for that position, by coalition building, keeping the peace, comforting those in pain, etc. It's entirely different than this frankly wacko idea of being an alpha that some American men have.
