first - this question seems to be trolling, both in its language and in its content. but since this topic hasn't been fleshed out here much, i will continue on the premise of good faith. for the moment. this answer is not going to be a tome, so it doesn't go into sufficient detail about the complexities around gender vs sex, etc... which if the questioner actually *cares* about this question, would be worthwhile to look into.
a. patriarchy is in fact that big of a problem. women (and women-identified people, which includes tons of people, including entirely straight men in certain contexts) are still attacked as women, paid significantly less then men for same type of work, devalued in many levels of society (politics, etc), ignored, trivialized, etc.
that is just on the bare surface level. if you consider patriarchy to be the thing that keeps us locked in gender binary, which many feminists (and anarchists) do, then the fact that most of us don't get to have the kinds of relationships that we want, or be the people we want to be, regardless of our gender/sex, is based on patriarchy.
b. there are as many kinds of feminists as there are of anarchists (probably more, actually).
c. since on one level feminists are saying that the standard way of doing things is a problem because of inherited and recreated hierarchies that don't allow people our full expression, then yes, feminism and anarchy can be seen as intimately related. on the other hand, some feminists just want there to be more women in government, so those feminists have nothing in common with anarchists.
d. calling feminists whiny makes me want to hit you in the face.
e. while identity politics (the idea that a particular identity is a fundamental issue that is worth organizing around - and *can be* organized around) has a lot of problems and weaknesses, it is one of the easiest ways to (start to) look at many of the inequities of the system we live in. many people get to that stage and make a home there, replicating power trips that mirror (as in reverse-image) the dynamics in the larger society. those people are particularly prone to contradictions in what they are asking for (treat me the same *and* treat me different). however sometimes what appear to be contradictions are taking into account the different contexts of women and men. for example, what self-defense looks like for women vs what it looks like for men can be significantly different, since women and men are mostly socialized with diametrically opposed understandings of physical violence.