In gender studies when criticizing power structures, folks ought meet the following criteria:

1) Be specific bout the power structure.
2) Demonstrate that there is a meaningful asymmetry predicated upon gender/sex.
3) Show that the asymmetry is not justified.

These are what my gender studies profs taught me fwiw.

Folks in the discourses I typically see make claims of the '2' variety. They note, in other words, that there is some asymmetry between the genders or sexes. From this they assume outright that they have satisfied both '1' and '3', they usually have not. Those '1' and '3' claims are where much of the discourse and disagreements happen.

Regarding '1'; Folks can oft critically attack a poor position thusly. Saying something like 'you need to be specific bout what power structure you are referring to'. For instance, saying 'patriarchy' is not a specification of the claim. Nor for that matter would 'matriarchy'. These terms refer to broad and overarching sorts of structures, not specific power structures as they manifest themselves in the real world.

In other words, there may be specific instantiations of patriarchy or matriarchy, but those are not themselves the category 'patriarchy' or 'matriarchy'. Folks have to make more specific claims than merely 'patriarchy' or 'matriarchy'. To be blunt, if they are relying on those sorts of categorical power structures to make their claim, their claim is incredibly weak.

This would be like saying 'its capitalism', true! But how? In what way exactly? Describe it.

If they cannot, well, the claim is not being justified, and is likely just an emotive expressing of an overly generalized disposition.

A lot of action happens with '1' in discourses. Discussing the details of what someone means, asking questions for clarifications to what they mean. Be nice people! Be Kind with it! No need to be an ass bout it. But, hold their feet to the fire, and keep an open mind. There are real criticisms out there.

Regarding '3'; this seems to be a very big problem in the current discourses. Folks assume, wrongly, that if they show '1' and '2' that therefore they've actually made the argument. They have not. I rarely see discussions reach this point fwiw, tho doing so is pretty critical

It can and indeed oft enough is the case that there ought be asymmetries in a system. There are actual real differences between the sexes and genders, and there is meaningfulness in having differentiations between folks more generally. It could be, in other words, entirely just, good and proper to have a power inequality predicated upon sex and/or gender (or many other metrics for that matter, but here we are primarily focusing on sex and gender).

This aspect touches far more upon the realms of philosophy than gender studies, and tbh is partly why it rarely gets reached by folks. What is just? What is good? These are very different sorts of questions. But that is how to approach the problem in the discourses y'all have. I also suspect that for gender studies folks in particular this is likely a difficult thing for them, as they too oft assume that '1' and '2' make the argument, and take somewhat naive positions on the ethics of it all. Such as, for instance, hedonistic ethics, consequentialist ethics, assumptions of pure equality as being sufficient, and utilitarian ethics.

Be kind with people, people!

Each of these have well known flaws with them, and folks that use them without serious criticism of them tend towards mistaking '1' and '2' as being sufficient explanators of the relevant ethics.

For instance, 'this job, sport, club, activity, etc...' (the specification of the entity and the power structure thereof), is disproportionately populated by men, women, queer people, etc... (the asymmetry of the distribution of said power structure), therefore there is a bad happening (the flawed ethic).

A lot of the meat of the matter is actually in '3'. I give here no furtherance as to how to go bout determining '3', beyond noting that the common ethical dispositions used are clearly and seriously flawed and insufficient for the tasks at hand. The point here really is to draw your interlocutor into the discussion along those grounds, while avoiding the temptation of relying upon the seriously flawed ethical dispositions previously alluded to.

This not because it would take too long, or there aren't some other solutions available, but because the online format presents an opportunity for folks to develop something by way of open intercultural dialog on a mass scale that simply wasn't available before. I am genuinely interested in seeing what pops up from such discussions....