Well, I forget where I first encountered the idea that hate is not the polar opposite of love (which is actually one of a number of things, depending on whom you ask), but it might prove insightful here. Jens, the way you've phrased the question is a bit difficult for me to follow, but it seems like you're trying to assert the difference in meaning between "sexism" and "gender-hate" (misandry/-ogyny). What hate and love have in common, perhaps, is a quality you might call "relational passion," in which strong feelings are created out of the interaction between two or more people - generated, figuratively speaking, by the third quantity "we." Whereas, with proper bigotry (sexism, racism, etc.), the generator comes from within the self and the emotions center around identity formation - in this case, through opposition. Usually, I think, there is some connection to a power relationship, i.e. the bigot sees him/herself as the rightful (if not acting) superior to the other party, by means of some convenient rationale. In love/hate, the other is known; in bigotry the other is unknown. This makes the existence of "gender-hate" rather impossible to imagine and surely the mark of a delusional character; one could not possibly know and have a relationship with every single person of a particular sex. In common, everyday usage, I'd say that "misandry/-ogyny" was more or less synonymous with "sexism," but I think there is an interesting distinction to be made.
This may be unnecessarily literary, but the written tradition labeled the "querelles des femmes" (I can't believe there isn't a wikipedia article devoted to it!) thrived for much of the Renaissance. Sometimes an argument between male and female writers on the merits and pitfalls of the female species (but mostly between male and male writers arguing over which aspects they disliked most), it provides, I think, an excellent example of a variety of opinions that are mostly sexist and which range into the misogynistic (and perhaps even the misandric - I'm not that well acquainted).
(Sorry - I get a bit pedantic
afterduring a few drinks)