Where I come from men’s clubs are illegal. So yes, like it or not it’s already been proven to have happened.

Could you provide more context please? Where is it you come from where men's clubs are illegal? And what are the reasons for them being illegal?

I like how you think know what all women have ever done though.

First of all, I'm sorry. It seems I've misread your comment. I thought you were generalising, which I find usually wrong to do. Especially in such rather sensitive contexts like these. That's why I've put "they" in quotation marks in my previous comment in order to counter that generalisation. But after re-reading, I've noticed that you've written "some women" not women in general. So I'm going to revise that part. (After I've sent this comment I will also strike the coresponding sections in my previous comment.)

Regarding your experience with your housemate, needless to say that this was shitty of her and certainly not a meaningful approach to improve mental health of men.

I'm not sure whether it's relevant now anymore to reply to the remaining parts of your response, but I'll do so anyway in case this is still relevant to you:

Here’s a genuine question. Why do you, my housemates, other women think they know absolutely what is best for mental mental health when it goes against what men even say? [...]

I don't claim to know what is best. But I claim that there are detrimental mindsets deeply rooted into our society which is severly problematic for the mental health of men. That's what's usually also refered to as "toxic masculinity". For different reasons I therefore think that a shift in how we are raising men and dealing with men's mental health is necessary. Those reasons include, but are not limited to, the following:

• I'm a man myself. Having experienced that pressure from my parents, some teachers, peers and basically society in general, has left me to this day with the feeling of shame when I'm feeling low. Gladly, I took the step to seek therapy due to a lot of shit that has happened in my life. But it clearly cristalises that - currently - I can't accept for myself that it's okay to have negative emotions and seek help or talk to others about that. It's much better than in the past, but it's so deeply burnt into my mind that it is still an obstacle a lot of times.
  I have no issues in accepting that in other men or people in general. To the contrary, I encourage everyone not to feel ashamed about how they feel, that it's okay, etc.. Because I know from first hand experience how bad this can be, especially if you've got a lot of other issues anyway.
• Sometimes I volunteer in supporting people who seek help with their issues in life or mental health. Sometimes it's stuff like "suicide watch". I've also got cases among my friends where I see that pattern repeating: If people don't deal with their shit, it usually has bad consequences in the long run. And among men is a high prevalence of cases which simply don't seek help and can't really deal with their issues in a longterm beneficial way. Men are usually experiencing high difficulties with even talking about such matters. This has also been observed in several studies and is - as far as I know - a well-known phenomenon among psychologists.
• I am in therapy and my therapists basically confirmed that.

To avoid a misunderstanding, let me make one thing very clear:
I am not against men having their "guy stuff", meeting in their interest groups and doing the stuff they like together. To the contrary, this is really good stuff! It's much better than sitting alone in the dark like a lot of depressed people do, myself included. It is usually very beneficial and helpful. (Depending of course also on stuff like the "social battery" of individuals.)
Psychological therapy for depression is in some parts also about finding what someone brings joy and developing some base stabilisation which helps them to go for that. In other words, men, who go to therapy, are also asked what they would like to do, what makes them feel good and so on. And therapists can help to enforce such mentally beneficial behaviours. Having a functioning social life is certainly one of the big factors. Distraction is also not always bad, it is also sometimes even encouraged. Now comes the,

But:

If men, despite enjoying such things, have concurrent issues, and such distractions and activies rather become a manifestation of "running away" or avoidance in general, those issues usually won't go away. Those issues will still linger and for each passing day may get worse and worse until those people - and this is regardless of gender - develop further dysfunctionalities which become increasingly difficult to deal with. And with men, as I said, it is usually difficult to get them to "deal with their stuff" due such reasons as toxic masculinity. Heck, it took over a decade until I got myself to seek therapy and I am angry with myself that I didn't do it much earlier.

Going on:

I’ve got a lot more support from men than I have from women. And I’ve seen guys get a lot more hurtful abuse from women than I have from men. But that goes against the narrative that all issues in the world are caused by the patriarchy and that women can do no wrong.

Good for you, that you got supportive men around you! Women are also people and people can be assholes. I'm sorry for you and the other guys who have seen abuse.

That certainly depends on the people though. Be among toxic men, get rekt. Be among toxic women, get rekt. Be among nice and empathetic men/women, and it's the other way around. However, toxic masculinity is a thing and there is plenty of evidence that men have usually more issues with dealing with their issues than women. As I've noted in my other comment before, that doesn't necessarily has a causal relation relationship. You can have patriarchy, which systematically treats women as "less" in various aspects, and you can have toxic masculinity, where men and sometimes also women make life hard for other men. The one does not necessarily cause the other as they can, but must not, co-exist independently.

I think the one take-away for everyone is: don't be an asshole.

If the suicide rate is so high for men maybe we should start by asking men what they need? How would having women telling them everything that they have done wrong a good thing?

The problem is, that a lot of men don't talk much about what they need, though. It's difficult to even get them there. But if they do, then sure, as long as we can make sure that such behaviour is not that kind of avoidance I mentioned earlier. Women are raised differently and are therefore usually (not generally) better in dealing with such issues and providing empathetic support. However, I don't think we should listen to one gender only, as gender alone does not necessitate virtue. Regarding mental health, I think we should listen to two parties: 1. the affected person and 2. the experts, which are mostly psychologists.

What women cannot understand is men are different to women. We act in a different way to you and that’s perfectly okay. What is not okay is women telling men how they need to act.

I'm sure that there are a plethora of women out there who don't have issues in understanding that men and women are different. That's an uncautious generalisation of you there.
Also, I'm a man, my dude. ;)
"One telling the other how to act" must not be a bad thing if it comes from a good place. If we regularly see how men are systematically struggling worse than women with mental health issues, then it's surely in their best interest to start pushing for beneficial changes. What those changes are, should be left to the experts though, and not to gender differences among people. Despite that, I think that it wouldn't hurt if a lot of men (those, struggling with opening up and dealing with their issues) would take some inspiration from women or people in general who have it easier with that.

Also if you want to do a bit of reading go find all the questions on the internet to the effect of “why don’t you open up to your girlfriend” and you can hear all the horrific ways women use men’s vulnerability against them. You can see the general consensus being that more often than not opening up to women makes things worse because of how women react to a vulnerable man and that if you need to talk about problems do it with men.

Well, that's surely shitty. But not the general consensus I noticed, nor the one observed in studies. Mind that looking for such questions is already a bias in the data itself. We can already estimate intuitively that those, who talk about difficulties in talking to their girlfriend/spouse are more likely to be in a toxic relationship itself or in one where miscommunication on both sides may be a problem. Look for the same question the other way around and you'll probably get a similar picture. This also doesn't equate to all the cases where such interactions with women don't have negative outcomes. Mainly, because people usually don't go on the internet and tell them how well their relationship is or how much they enjoyed talking to their women-friends. So, to get the full picture, representative surveys must be conducted. This also fully neglects the plethora of men who don't even talk at all to anyone, which is, as far as I know, the much higher number of cases.