I don't think feminism is the wrong word in this case. The way men are harmed by patriarchy is directly related to how women are understood as lesser. Male only drafts, male worth based on possession of women, unequal familial rights, and harmful beliefs about men's emotion all exists as ways to subjugate women.

For the draft and emotions, men's "violent nature" is cultivated because "we have to protect the women." The only emotion you allowed to have is righteous anger used to defend women. This dynamic ties neatly into men as predators. Men are naturally violent, look at how that violence protects the women, but when improperly raised they become monsters.

Men often feel as though they have no social standing if they haven't had sex with a woman. The way that relationship is framed is often conquest and power rather than mutual connection and understanding. The truth is men would benefit far more from connection, understanding, and knowing that they can have social standing beyond fucking somebody.

Unequal family rights are directly related to the societal expectation that women are the primary care givers. Which frequently results in women working full time jobs, taking care of the children, and taking care of the house.

I don't think the term feminism is really the problem. Billions of dollars have been spent by right wing billionaires to control this narrative. It's no wonder young people have a skewed perception of what feminism is. I don't think changing the term to gender equality really would have helped much.