He didn't mean antonym, which is why he mentioned at the end girls could then find both a nice and strong guy. In other words, it's less likely for nice guys to have the trait, but not impossible: they don't have it because they didn't attempt it since they simply listened to girls who didn't know (or weren't willing to admit) what they wanted.

In my experience, girls do want first and foremost an alpha male, and being a nice guy on top of that makes it even better. It's just not a necessity so the jerks can succeed without that quality, whereas the nice guys can't succeed without "dominance."