I didn't say that most institutional structures aren't dominated by men. I don't know whether "most" are or aren't -- neither do you. If you figure out a way to quantify that, let me know. Seems like a research grant in the making.
I do know, however, that "every other organization is a men's organization" is a ridiculous statement. Every other organization? Seriously? In order for that to be true, "men's organization" has to be defined in some absolutely meaningless manner where organizations which include women and have women as administrators and are run by women are somehow oppressive "men's organizations". Otherwise the statement is provably false and anyone caught saying it should be instantly discredited.
>It's the positions of power being dominated by men that makes the institution for men
First off, very few men have access to those positions of power. Men who don't have access to powerful offices still have issues and need protection. If you weren't born rich and to parents with connections, you likely aren't becoming a surgeon general or president or even university president. So in what universe can the entire university be termed a "men's club"? Where do the men without access to institutional power turn for relief? They are not only excluded from what feminists term the "men's club", feminists fight to disallow them from forming groups to fight for their own interests. Double whammy. Lower-class men get universally screwed over in the blind drive to bring "equality" to positions of power.
Second, much of feminism ignores the question of why one-to-one gender representation is desirable in the first place for each and every position of power. Why is it a goal in and of itself? In hiring someone to lead an organization, I want the person with the qualifications that best match the job description to be hired. If that turns out to be a man, great. A woman, great. I don't care. There is a job that needs to be done and it should be done well, free from political or ideological influence.
There is the argument that even if hiring is completely gender-neutral, if the most qualified people turn out disproportionally men then it is inevitable that male interests will be baked into the system. Well, the man is still the most objectively skilled person for the job maybe you should figure out how to build control mechanisms that prevent male ideologies from perpetuating insidious effects throughout the system, rather than just scream about how men should be barred from the position. Just saying "let's hire more women because they're women" seems like the laziest possible pseudo-solution and doesn't seem to lead to desirable long-term effects. Do we want people running our society who are qualified to do so, or do we want people running society because of gender quotas?
Third, there is the question of whether or not these inequalities are systemic because of male oppression or female behavior. It is likely a mix of the two, but feminists completely discount the latter. For example having children is a pretty strong biological drive in human beings. I'm not saying all women want to have children, but a lot do. So maybe some females aren't taking high-powered high-strung positions because they'd rather have kids. The vast majority of high-responsibility positions can't cope with the candidate taking 5 months off for mat leave.
There's the issue of "oh the females only want kids because they're socially programmed to slave away as subservient housewives". I don't know, the nuclear family is a pretty strong element of culture and socialization for sure. But it seems unlikely that given our million-plus-year history of a biological drive to have kids that it's all a social construct. Further, that females only have kids because they're brainwashed seems unprovable.
There are innumerable other issues I could list but what's common to all of them, in my view, is that they focus so intently on the end goal of elevating women's power status that they bulldoze over all other considerations indiscriminately.
We need nuance in order to achieve an actual egalitarian society, which much of feminism -- especially statements like "all other organizations are men's organizations" -- beats into the ground with a thousand-pound shovel.