This part of the puzzle needs to be addressed too in order for equal rights to proceed. Sometimes it’s framed as if men and women are on opposing sides in the question of equal rights, but I’ve found that more often than not the very SAME mechanisms (i.e. old-fashioned patriarchal ideas about the “proper role” for the genders) that lead to women being discriminated and opressed in some roles (for example as employees), lead to the same outcome for men in roles that are traditionally seen as female. I guess the most important example of such roles is being a parent.