The fact is you guys are using really loaded vocabulary, and in a way that is really confusing too.
Either "Feminism" is the movement where women fight for their rights and interests, or it is the fight for equality between genders in general. It can't be both. Or rather it can be both, but you have to explicitely state which one you're refering to everytime, otherwise you're just blurring the discussion voluntarily or not. In any case asking men to rally under feminism to defend their rights is completely futile, even if you were to somehow make feminism solely about equality between genders the movement is historically completely owned by women.
It is both. I don't see a distinction between the two.
Either "Patriarchy" is the system that promotes male superiority in society or it is the sum of all gender imbalances in society. These two things are not the same at all. Matriarchal societies exist, and they have different roles for each gender, simply women tend to dominate in them. Are you going to say that what is causing the difference between genders in a matriarchal society is the Patriarchy? That kind of makes no sense.
Patriarchy is the system that promotes male superiority in society, but it
also can be used to explain problems that face men as well. Not all men are winners under patriarchy; they are only winners relative to women. The argument feminists make is that while men might be better off than women in relative terms under patriarchy, it makes them worse off in absolute terms.
I'm sure a matriarchal system would present problems all its own, but we aren't advocating a move to a matriarchal system.
So when you guys are saying that the idea that all men are pedophiles for example comes from the "patriarchal society", you have to be more clear. Are you saying that classic patriarchy (like in a society were men are dominating) is producing this phenomenon? In this case you are wrong. Classic patriarchy promotes the idea that men are strong, this phenomenon comes from the idea that men are predators. If anything it has a lot more to do with feminist literature than classic patriarchy. Sexual violence, especially toward children, was way more prevalent in old patriarchal societies, but this pedophilia hysteria was nowhere near as strong as right now.
I honestly have no idea what the connection is between this stereotyping of men and feminism or patriarchy is, if anything. And I am at work so I can't really research it; I'll have to punt on this point.
Finally the idea that either ideology, feminism or manism, is just a fight for equality is just naive. Take reproductive rights : women and men will never have equal rights in this field, simply because one gender carries the baby for nine months in their belly, and the other doesn't. What you are looking for here is a balance between the rights for each gender, which is not the same thing as each gender having the same rights. By definition every advance made by one gender in this field is made by taking away some of the rights (or privilege if you think these rights are not rights) of the other gender, so the healthy way of carrying this process is for each gender to push for their advantage, so that when the dust settles everyone hopefully meets somewhere in the middle.
Masculinism is probably the term you are looking for
I don't quite agree with your construction of this. I would agree that in the case of reproductive rights, women will have "more" because they are more directly impacted by it (and it directly involves their decisions with their own bodies), but I disagree with your characterization of it overall. This is not a zero-sum situation where if women gain, men necessarily lose. As I said before, men might lose
relative advantage, but in absolute terms both men and women should gain. For instance, if men and women were to share the load of household chores and raising children more easily, men might lose relative privilege (not having to do as many chores), but they receive absolute benefits (men in relationships with more egalitarian levels of work-sharing report higher levels of happiness).
In a certain sense, it is about creating balance, but I think that the way you construct it, it appears that men are losing something, rather than gaining something. You frame it as an inherently antagonistic process when it does not have to be.
(Sorry if this is slightly incoherent; I'm trying to write while talking to a customer)