What is the synonym/antonym for "feminist"/"feminism"?

Etymologically "Feminism" is derived from "female" and historically it has referred to women's rights. But the term — as a sociological term as well as a social movement — has evolved in many ways, so while for some "feminism" is the struggle for women's rights in society, others will explain that feminism is the struggle to remove gender-biases from society, and as such applies to men's rights as well as women's.

So when you're looking for the complementary term to feminism, you need to know exactly which meaning of feminism you're going for, because in many contexts "feminism" might be enough for you.

Also, it should be noted that even if we find a term that says "mens' rights" to complement feminism as womens' rights, they will never be entirely parallel in tone and connotation, because mens' rights and women's rights aren't symmetrical. If (some versions of) feminism describes itself as the struggle to achieve equal rights in a male-dominated world, a totally equivalent term would have to imply a similar male struggle, which is, well, a bit of a stretch.

There is an ostensible but in the end untenable male counterpart to feminism, namely

Masculinism

but because of the long history of feminism and the much shorter and shallower history of masculinism, and fairly different agendas, it'd be difficult to call them perfect pairs.

The suggestion of this word is only to express that in at least one direction there is a corresponding term for males that is superficially appropriate.

Feminism is (terribly oversimplified) a movement that is directed towards equalizing the power and rights of women to that of men, given that they are almost universally allowed little power and few rights. Masculinism is not the same concept replacing 'women' with 'men', rather it is more of an intellectual reaction to feminism, trying to increase awareness of where feminism has restricted the rights of males. There is a perception by some that power and rights is a zero-sum game and that gains by one is a loss by the other.

Though this theoretically might be the case, the surface meaning of masculinism might lead one to use it as a counterpart to feminism, the term seems closer in practice to reactive male chauvinism and misogyny.

I don’t believe that there is a direct masculine equivalent for feminist, because it’s a fight for the rights of a discriminated group and this is not the case of men.

But if it helps you, there is a generic word for those who oppose any kind of gender discrimination: anti-sexist.

While this might be too basic and directly answerable a question for this venue, you might be looking for misogynist/misogyny. It has a different connotation, but there haven't been enough English-speaking, female-dominated societies for us to have come up with a positive word for it.