"Gender equality" isn't gender-specific, yet FEM-inism quite often claims that's what it's about.

Feminism is (1) the advocacy of women's rights (2) on the ground of the equality of the sexes. Both the Oxford dictionary and common usage would point in a direction where are TWO elements of the definition, not one.

It's not vaguely and broadly about "equality". It's narrowly about an angle from which a subset of goals on the "equality" spectrum is targeted. Feminism definitionally focuses on women and gauges its achievements based off changes the women's status in a society - but it does so from a core doctrine of social, political, and economic equality of the sexes. In other words, it's simultaneously about "stuff for women" and about "women should have the stuff because we want to bring about a world in which they're men's social, political, and economic equals - and we believe they currently aren't those, or aren't sufficiently, in [insert areas] because [insert feminist lenses of looking at what's wrong with the world]".

When dissected, the definition of feminism seems (to me) rather adequate given its actual history, goals, and projects. Yes, it's "about women" - or at least prioritarily about women and "methodologically" about women - not an analysis based off other demographics. And yes, it's about this demographic's status and interests within an optics of "equality".

I don't understand what's the problem here and why the word "feminism" is such a devil in the English-speaking countries. It's one reading of society from one angle - and an angle that has, historically, in some people's views, been unjustly neglected [insert feminist historical and textual scholarship where this is argued and analyzed], creating a lopsided society in terms of who gets to speak, on whose behalf, and to create social and legal norms around which power is concentrated. Double the reason why people who accept this idea should insist on this term.

Enter "patriarchy" as the descriptor of the essential features of the system and of the mechanism of their generational reproduction. It's, again, a fitting word to designate a world of varying degrees of female legal minority, male-line inheritance (including symbolic inheritance through name, status etc.), and the social norms that form around it. I can't think of a more fitting word than "patriarchy" for this concept: the gendering is neither arbitrary nor even unnecessary to synthesize what's communicated.

Both "feminism" and "patriarchy" are highly adequate words for what they aim to describe. I couldn't use anything else, that doesn't result in a lot of circumventing and paraphrase, to talk about these things - although I may, occasionally, need to qualify and clarify terms that remain broader than my specific point might be. In a less generalist discussion, I may need to specify which of the approaches under the conceptual umbrella of "feminism" I have in mind. If I wish to focus on a specific element of legal minority, I may need narrower terms than "patriarchy". But on the whole, in a generalist discussion with reasonably educated people, those are appropriate terms - appropriate academically, appropriate historically, and as good as it gets linguistically to squeeze the messy and the complicated into a single label.

Now, contrast this against "congressmen". Unless the principal acceptation of the word "man" broadly retains its sex-neutrality, and I can reasonably rely on this being a common intuition, the term isn't appropriate. My intuitions on how English develops are limited, because I'm neither a native speaker nor live in a society where I primarily function in it, but it would seem to me that the language has developed beyond that, and that these terms are sometimes marked the way they aren't necessarily marked in other languages. I still talk about "droits de l'homme" in French to say "human rights" without batting an eyelid - but I wouldn't talk of "rights of men" in English to convey the same concept. All of this is somewhere elastic, and the langauge - any language - develops unevenly and even contradictorily, but in English I feel that it would be provocatorily marked the way that it simply isn't in French.

Same as with my usage of the sex-neutral "he". A part of me really dislikes "they", so it's also an aesthetic preference, but a part of me is acutely aware of the fact that if I insist on "he" - as much as I may be simply guided by my internal feeling of what's "good English" and nothing else - today it's going to be marked in ways in which it wasn't before. And speaking consistently "like that", with such now-marked linguistic choices, I'm more likely than not to "send messages" about ideological positions which, ironically, I don't hold. So it's a risk, in ways in which it isn't in other languages I speak, even if those have been increasingly gender-neutralized too. Yet sometimes, a certain article of that neutralization is going to feel awkwardly "forced" in them, even when the English equivalent is completely natural. There's no cut and dried rule around this.

Yet, I think that people know. In every language, this is largely - even if imperfectly - one of those "I know it when I see it" things, when you read/listen to somebody at length. I think people can tell innocence, deliberate anachronism, and/or purely stylistic choices from provocation, deliberate equivocation, and/or purely ideological choices, quite well on the whole. People can tell an attempt at conceptual precision from an attempt at obfuscation even if the words that are being used in both cases are the "same" words.