You're drawing a false dichotomy. The third option (other than going to his manager or being a jerk) would have been to realize that not everyone at work is going to be his friend, and not complain about feeling uncomfortable because this woman wasn't acting towards him in the way he assumed she should.

A mature person would only complain to his manager about someone's behavior if it was clearly in violation of societal norms (hostile, racist, sexist, etc.). Feeling vaguely uncomfortable about somebody doesn't fall into that category.