...tbh though, I think you're not framing the situation correctly:
Women for a long time were excluded from male dominated spaces. So they ended up having to form their own groups and spaces. Now you imply that women having those spaces is the exact same thing as men excluding women from their spaces.
Yes, the loaded word patriarchy is a thing that hurts both men and women. But trying to frame men and women's situations as analogous is ignoring a loooot of history. You're looking at the end result and measuring it without seeing the past circumstances that created it.
This is like looking at the Black Lives Matter and being upset that they didn't name themselves All Lives Matter. When their creation was a direct result of black people losing their lives at the hands of police, and the name was meant to bring attention to that.
Women's groups and spaces, similarly, are a direct result of wanting to escape the discrimination and exclusion that comes from being in male-dominated environments. This is not 1:1 with men excluding women from things. Not when historically, women have been excluded from: voting, having paid jobs, having their own bank accounts, owning property, the choice whether to have kids, the choice of who to marry. Not to mention, literally being considered property to be bought and sold through dowries. For hundreds of years up until very recently this was the case. And the scars of that still exist in society. You cannot look at those scars and be blind to the history.
Men are definitely less likely to report rape if they've experienced it. In part rape is still seen as something to be ashamed of being a survivor of. I'm not arguing against that. But idk man, I think you're making a lot of black and white assumptions here about why things are the way that they are.