To me, it seems obvious that there hasn't previously been a male counterpart to the feminism movement because men haven't been institutionally lower-status the way that women have been.

What does it mean to say that women are "institutionally lower-status" than men, and what is the metric for institutional status? This notion is counter-intuitive to me, because I think there are multiple institutions and multiple dimensions of status. Although I think it's plausible that men were indeed institutionally higher-status in many cultures throughout history, specifying why is actually a nontrivial philosophical problem that I don't feel feminists have thoroughly confronted.

For example, in Colombia, institutions may grant males more prestige, yet grant women more protection. Which gender has more "status" depends on whether your metric of status is something like "who is more likely to be in charge of the household," or "who is more likely to die horrible deaths to chainsaws or machetes." I'm not sure how we we can aggregate these metrics, considering how dramatically different the units are; it's kind of like adding up feet and pounds. Do dead men have status?