I'm not sure if we're a matriarchy yet-- globally I really don't think that this is true, but I do agree about feminism.
It's a woman-led movement that only concerns itself with women, and if men join they are expected to support women's interests and keep their own interests to themselves-- or at the very least, it seems like they're expected to defer to the superior insights of women, even when it comes to who they are and what they should want. The idea that men's rights groups are hate groups shows how rabid feminists can be-- they're completely ignorant of the movements and come off as simply being uncomfortable with the idea that men should have a voice, as if they've 'lost the right' because of the fact that they're natural villains, exploiters, oppressors, etc.
I see these two movements as reflections of each other, though I think that the men's rights movement is largely a reaction to the exclusive nature of the women's movement-- it's for men who are interested in defining themselves in the new society that feminism has helped create (well, thinks it has helped to create... I think it's probably happened for more business/political reasons)... feminists are directly responsible for its existence by embracing exclusivity and radicalism and showing complete disregard for men in the feminist 'utopia' that they hope to create.
To me it just seems logical that men should have a role in their own identities/rights, it doesn't mean that they should just sit around and hate on women but the fact that feminists are only concerned with themselves, don't understand or even despise the opposite sex and aren't interested in understanding them (the whole fascist caveat of 'they're the enemy, we don't NEED to know them', basically a dehumanization strategy designed to support their ridiculously biased historical narrative) means that the Men's rights movement does have validity and they shouldn't be demonized. At least until there's some sort of compromise and the two merge to form a humanistic movement where everyone respects and supports each other and nobody has any more validity than anyone else.