Zeta male refers to the 4th social hierarchy position among males. (alpha - top, beta - second, omega - the rest). Zeta males consciously reject a the traditional social position as it is based on how they are valued by women. Zeta's can be straight, bi or gay.
I asked Jim to buy be a drink and he said I should pay for it myself. I guess he's a Zeta Male
Not a thing. If you judge someone based entirely on their sex; it's just plain old sexism.
Sometimes used to suggest that sexism can only go one way (say, males can only be sexist against females) and that if a male experiences sexism it's not really sexism; it's reverse sexism. Or the opposite of sexism.
This is designed to downplay or justify the sexism the male is experiencing.
As a term, reverse sexism is as realistic as reverse theft. A Klan member may suggest that if a white person steals from a black person it's reverse theft.
I understand that you are being denied access to the domestic violence shelter because you're a man, but that's NOT sexism; it's only reverse sexism.