I don't think this is true in the slightest. I think women have a pathological fear of the very real and often very violent reactions to them attempting to exercise any power in an overt and coded as "masculine" way. That's why thousands of years of women learned how to wield power in subtle ways that did not draw male anger. Women litigators and others in very male coded professions have to walk a very fine line of appearing sufficiently tough and competent but still remaining sufficiently "feminine" or they get shredded for it. We hear about this every fucking election cycle - the endless commentary about woman candidates and if they are likeable enough, when absolutely nobody talks about that with men.
Exorting women to deprogram themselves as the primary solution when there are extreme levels of backlash and social consequence to doing that is impractical and unfair. You're making the slaves responsible for the violence of the masters. Patriarchy is a DOMINANCE hierarchy. That means the people who are higher up the social pyramid and who have more institutional power have a much greater responsibility to shift and change norms to be more equitable. They need to take themselves on before they demand that those they oppress do things differently.
Male aggression, male domination of others and control of women in particular are at the root of pretty much all of our social ills. Making the victims of that primarily responsible for interrupting it is just an excuse so that men don't have to do the work they very demonstrably need to be doing. Sure, women have some work to do around internalized patriarchy, but what you are suggesting is like making Black folks primarily responsible for interrupting racism. I'm not saying it's easy for men to deprogram themselves either, but they are the dominant social class, and they have the vast majority of institutional power. If men got together and took that shit on, even if it was just 30% of men, it would have a huge social impact. We've already seen the hints of that in the past 50 years. Younger men are much more involved in sharing chores and being involved with children than they used to be. They are already much less likely to have the extreme levels of stoicism that their father's generations were expected to have. Men need to keep that going - and yes, women need to let them, but most women want that. Some don't, some need to do a lot more work on letting men show vulnerability, etc., but there are also plenty of women who really want that. And believe me, there are plenty of women who want to be left alone to be strong leaders without having to walk a tightrope of social acceptability.
A 2001 poll in the United States found that 80 percent of women in their twenties believed that having a husband who can talk about his feelings was more important than having one who makes a good living. And that was over 20 years ago - so that impulse has only grown. There's all sorts of research that indicates that is the case. Women uphold patriarchy too, but they are not the top of the dominance hierarchy pyramid. I think it's important to keep that in mind. Deeply entrenched and institutionalized power differentials have a huge impact. Just 50 years ago in the US, women had hundreds of fewer rights under law. Sure, we all have to work together, but not by pretending that these social dynamics don't exist.
