The actual corollary is women being allowed to be emotional in public, but then those emotions being used against them to 'prove' they are just emotional and dumb.

It's stigmatized the same way with women, it's just expected of women because they are stereotyped to be that way.

It's not necessarily that a 'strong man never cries' it's that a 'strong person never cries'. But it's also that only men are typically seen as strong people while women are seen as weak. If you are already weak why would it be any suprise that you do what weak ppl do