I don't think you're wrong that men are going through their own struggles.
The thing that is probably a sticking point is that a lot of the structures that support women in the modern world are largely created and maintained by the work of women. Like, the food pantries and the foster care I went through was skewed much more heavily with women doing probably 75%+ of the work in the organizations (some of them closer to like 98% of the work), both for the aspects that supported women specifically (programs for single mothers and such), and those who served both men and women (like food pantry or health services).
So the question is--why are men not banding together to support other men? You guys KNOW there's issues being neglected by society. So...where are all the men making organizations to socially support men going through mental health crisis? Why are you not looking at the women's organizations and taking notes and learning from how they're structured, and taking up those tools yourself to adapt to this situation?
I don't think it's true that men making an organization to help other men's mental health would be somehow driven into the ground by some group of evil feminists or something--the women I've seen working with "feet on the ground" for supportive organizations were not like that.
I think there'd be side-eyes if say, a new free mason organization popped up where businessmen are cutting deals in no-girls-allowed backrooms or something. The old rich-boy fraternal network of power, you know? Where people in positions of monetary or political power try to exclude others from that power?
But something genuinely out there to, say, talk with men struggling with mental health, or suicidal thoughts, and to talk incels out of being incels, and to promote a healthy way to cope with the changing world and the stress the world and "masculine" gender expectations put on people I think would get a bunch of big positive nods from the women I've known who've been volunteers for "women's organizations". Like--yes, it's definitely needed for you guys! And fundamentally a different sort of support network than the old-boys networks that feminists historically protest.
Like, there's a big difference between alcoholics anonymous and a college frat known for abusive hazing practices. There's a big difference between a group of vets talking together about their war experiences (like all the vet lodges for WWII and such), and a professional organization for people in a given career that doesn't (for example) admit female members. One type of organization focuses on the mental health and well being of its members, the other type of organization is hoarding power. It's the "hoarding power" types of organizations that feminists protest.
Another problem with helping men with mental health is that often men don't listen to women on certain topics. There seems to be a dire need for male leaders who will approach other men and talk with other men about these squishy, emotional things. Because one dude being an example is one of the few things that can get through to other dudes sometimes.
But there's a social stigma for men who are too "emotional" and "vulnerable", so it's hard to get volunteers for this to kick off the trend. But someone has to do it? And it's only something other men can do?
I think a lot, sometimes, about the Captain America scene where Steve is going/half-leading post-snap support group. It's a fictional example, but it basically showcases/envisions the type of leadership that needs to develop for dudes. And it's not a position a woman can easily step into, because plenty of guys who need help are already rejecting women for any variety of reasons (bitterness, resentment, fear, anxiety, whatever). Some guys need to step up to the plate and be like Captain America, on a local level, so local support groups for guys can happen.
I honestly don't think "women" would get in the way of an organization like this--or at least, the women in the circles I hang with wouldn't. I think it's more the lack of men willing to put their necks out there (judging by the gender imbalance in volunteer and support organizations I've been exposed to), because it's certain to get plenty of pushback and blowback and be hard work for little recognition and little pay.