I love mirrors. It's tough for some people to see their reflection, I guess.
I know some dogs and cats go nuts when they see themselves, thinking it’s another animal. It's about being self-aware.
My Labrador, Roxy, looks in the mirror and smiles because we showed her as a young puppy what the mirror was showing by waving and petting her while she looked into the mirror. It worked.
Anyway, I'm a man (or 20-year old male) and I'm not terrified of mirrors... so I think I disagree with your stereotype—but my best guess for why *some* men are afraid of mirrors may have something to do with sentience. Maybe some guys lack it and think it's another man starring at them?
Hope this helps :)