"My standard for sexism is: would it be OK to do it if the situations were reversed?"

This might not actually be a good test because, as a society, we have different social standards for men and women. While Kagan's actions could be considered "masculine", most likely if a woman did something similar it would be considered "bitchy".

Because we use different words and standards, it's really hard to truly reverse the situation.

By the way, your example indicates that you're confusing sexism and misogyny -- you could debate whether his position is misogynistic (expresses a hatred for women) but it seems fairly likely that it's sexist (makes some women feel uncomfortable in a situation because of their gender).