I've never been certain what people actually meant by 'male' and 'female', beyond the obvious physiological differences.

There are certain associations with 'outgoing' and 'introverted', 'dominant' and 'submissive', certain roles (women do regenerative work, men do profitable work), and certain specific behavioral tendencies (boys tend to play at group conflict, girls tend to play at social interaction), but the vast majority of cultural associations seem to be fairly arbitrary.

Beyond the associations is the idea that there are two categories, and it's very important that things be known to belong to one or the other. That's the part I cannot empathize with.