Next area for improving the debate: we can recognise the limitations of our intuitions.
Psychology can be hard to think about because aspects of our selves which feel essential - our feelings, interests, or abilities - are also consequences of our biology and social environment. It feels like my preference for wearing trousers is intimately tied up with me and my maleness, but I have to recognise that this is a fact contingent on my particular historical situation. Born a male Highlander or an ancient Roman I'd probably prefer to wear something else. Trouser preference is a trivial example, but things like my preferences in school subjects, games, sexual partners, hobbies are all contingent on my social environment. Maybe not entirely, but the question the psychology of sex differences must address is: to what extent?.
Arguments that "Men just prefer X" or "Women will always want to do Y" may be based on strong intuitions, but they have no explanatory currency.