Depends also on the context. If it relates to babies men will generally be submissive to women, recognizing women are the expert in that area with better outcomes likely.

If the family is under attack it will generally be the man that fronts.

The point being men and women are complementary and take the lead at different times depending on the situation.

Agree the whole dichotomy is rubbish and a fad spawned by socialist leaning universities that we must all live through until they realize it is just wrong.