Patriarchy isn't just about dominating women, it's about dominating everyone you can as a way to gain status and keep others from trying to knock you off of your rung in the hierarchy. It is very literally a dominance-based hierarchy system. The loneliness that this engenders (because you can't ever be close to anyone as they are all your competition) is a part of what is killing men right now. This dovetails nicely with the brutal brand of capitalism we practice in the US, so changing this system won't be easy, but all the more reason that we need men to lead the way.
Nothing at all wrong with healthy masculinity. I find it quite attractive and enjoyable - but I want a partner (fortunately, I have a good one) and not to be somebody's sidekick or mother stand-in. And, we live in a country where 50% of the people believe that the father is the "head of the family." I'm sure another large percentage of men and women too believe that to some extent subconsciously. This is the kind of stuff that we need to dismantle because it drives the beliefs that men have the right to control women and punish them when they resist being controlled. It drives the belief that women's bodies exist for men's pleasure. To get to a truly healthy society, we need to dismantle all the hierarchy based on immutable traits, but since that's a tall order, I'd settle for dismantling the gender hierarchy aspect for now.