I really appreciate all that you've said and I think that we are very much on the same page. I absolutely agree that women need to be doing their own healing work as well, although as I noted, this can be tricky when the wounds continue to be inflicted on a pretty much daily basis - with little support or empathy for that. And, I also know a lot of strong feminist women who have done and continue to work on their own healing, who do not dislike men (in fact, most of them actually love men, but can be a bit disappointed in them as a group). Women here on Medium such as Demeter Delune, Yael Wolfe, Carlyn Beccia, Patsy Ferguson and others hold culture to task, and at times, hold certain men to task, without it being shaming or demonizing. They catch a lot of flack for it mostly.
I completely agree that we've all got to turn our attention to the ways this society harms us all, but because violent domination of others and control of women in particular are core aspects of masculinity in this culture, I do think there's a special onus on men to deal with that. Perhaps I'm conflating what you are saying with what I've heard too many other men say in the past, which comes across as "Even as they continue to be oppressed and victimized, women need to rise above their pain and be more gracious and nicer about it all. Otherwise men won't do their part." I don't think that's exactly what you are saying, but it is something that I've heard an awful lot - something that essentially demands that women do not only their own healing work, but make it more comfortable and easier for men to do theirs, even as they continue to be harmed. Most violence against both women and men is perpetrated by men, most rape, against both women and men, is perpetrated by men, most of the sorts of domestic violence that involves control is perpetrated by men. Yes, women have work to do as well, but it's not exactly a situation where everyone is at equal fault (beyond the ways that we all allow this social system to go on unconfronted).
The Petersons and the Tates of the world arose in the first place because we did ask men to confront the ways that the Man Box is harmful and they really didn't want to. I don't know that asking them to do that in a more empathetic way actually moves the ball unless men take the lead in doing so. I'm all for finding ways to come together and to all work towards a better culture, but I honestly do not see any practical way for women to "speak more thoughtfully" to young men that won't immediately be dismissed as weak or self-serving or irrelevant. This is why I feel so strongly that men have to lead this charge. Every mainstream feminist organization I'm aware of does recognize that patriarchy hurts men, and believes that equality means freedom for everyone, not just women. But, their focus is primarily on the lives of women - where it belongs.
From what I could ascertain reading Katz's book, there is a fair amount of collaboration in the work that he and his organization does with "women's" organizations. But, as he also notes, men have to be careful to not try to take over, to not try to White Knight, or decide what is best for women without asking them what they want - and that often well-meaning men who go into women's spaces often do try to do exactly that. It's a place where there's room for improvement all around, but it reflects some of the larger issues of trying to grapple with this stuff in a still highly androcentric culture where men are socialized to be leaders, fixers, doers, and such, and to largely look at women as antecedents, even if only subconsciously.
The Gillette ad called on men to be strong leaders in creating a better future for us all, including our children. Their tag line was, "It's only by challenging ourselves to do more that we can get closer to our best." The very fact that this was seen as offensive is the entire problem in a nutshell. How are we supposed to talk about what needs to improve if it rattles male egos to hear that there is room for improvement and it pisses men off to see guys depicted doing the exact things that we want and need them to be doing?
Menfluencers asking men to take a good hard look at themselves and the way the culture shapes them are never going to be as popular as the men who offer scapegoats and don't require any deep work. But we need them anyhow, and we need them to figure out how to reach boys at very young ages, because that's when they are being recruited and radicalized online. Studies indicate that if boys have already been given a good foundation in the basics of and importance of equality they are less susceptible to the hate and the Tates. But that needs to become a mainstream fatherly activity then - and right now, it's not. It needs to be taught in the Boy Scouts, and in sports teams - and women need to support and allow that, but as of right now, masculinity is so constructed as the antithesis of feminine qualities, that asking boys to value those qualities and to embrace them at times is challenging without men first remaking masculinity.
Clearly, I don't have all the answers and I don't claim to, but I have thought quite a lot about all this in the past year, and been in many conversations about it, and the more I think about it, the more I believe men are going to have to figure this out for the benefit of men and wider society. Women need to support those changes, and not try to keep men in old boxes and norms, but we absolutely cannot do this for you.
All the feminists I know, including the ones mentioned above, do talk to men, in a reasonable and approachable way, on a daily basis. It mostly does not equate to more men realizing that feminists don't hate men because these guys want to have a scapegoat, they want to have a place to channel all of their discomfort and rage. They don't want to understand women's perspective, they don't want to come together. They don't want to indict patriarchy. They want women to make them feel better about themselves and to make them pay when they decline to do that.
This is pretty much my daily experience here on Medium, and it has been for over 5 years. Don't get me wrong, there are some great guys here, just as there are IRL, but they are for the most part, already on the side of a better world for us all. I don't know if I ever change very many minds. A few, that I'm aware of, but mostly, I think not. I've even gotten into some long and in depth conversations with guys that I tried to cultivate a personal relationship with so as to help them connect with me on a personal level and let me do that with them. Each and ever time, it has come back to bite me in the ass and I've ended up having to block the guy or dissociate from him because he was completely unable and unwilling to let go of his paradigm of blame and victimhood at the hands of women, no matter how much I tried to "reach across the aisle" and understand, sympathize, but also ask him to understand and sympathize with me.
Clearly, we can't improve the world unless we work together, but I'm just trying to point out to you that in my experience, it's not nearly as neat and straightforward as one might like it to be. Men have to make it cool to champion equality, rather than to engage in performative domination. They have to make it manly to do deep inner work and to grapple with insecurities - something that is completely antithetical to the way that masculinity is currently constructed. Until that happens, what women do or don't do will make little difference, I don't think.