From a purely pragmatic standpoint, I think it's generally much easier to convince a group to stop doing something because it's bad than to convince them that its okay when others do it, but only bad when they do it.

As to the other two, I believe the party line is that sexism requires both prejudice and institutionalized power in order to function, that males are uniformly more socially powerful, and thus that male-directed sexism is impossible. In itself that's little more than a definitional quibble, but in practice this shakes out to a belief that otherwise identical behaviors are less alienating when directed at men.

Would this imply that, in a truly sexually egalitarian society where niether side posses any systematic power disparities over the other, and both would be free to objectify the other without being sexist?