At least in a stereotypical sense, the girls club is generally a group of women talking shit about other people behind their backs, sometimes bullying other women to their faces. You don’t commonly hear about a workplace of mainly women sexually harassing the few men to the point of self harm or raping them.
The labels may be borne of patriarchal values, but the mind sets of the people IN these groups are too. In my opinion, you’re simply denying reality in favor of a progressive idea of how it should be.
The term “boy’s club” here is really not generalizing “men” or “boys” as a whole, but rather it’s by its usage criticizing the specific group mentality it describes, that of a group of “boys” who treat women with less respect than each other, or otherwise exclude said women, as in at least some cultures is common from some generally younger “boys” who haven’t really matured past a mentality usually developed from a young age, because they lack the experience to know it’s wrong.