First of all, lots of women are fine with men's emotions - and some aren't. We grew up with patriarchal norms as well, and those women need to keep challenging their own internalized patriarchy in order to let men be full human beings.

Secondly, the only reason that "men's issues' would piss off a woman is if it is very clearly trying to reinstate some old, outdated idea of how things "should" be - for example, this story. We absolutely should talk about men's loneliness but not by demanding that women solve that.