I think we need to understand the complexity of the gender debate, to truly understand, why and what we are supposed to do in this day and age.
The virtue is equality. Equality is virtue of gender, at least it has been this since Karl Marx deduced it from the platonic lore he read, and some of the descriptions that he read about Sparta, that is the ideal polis (city state) of communism.
Plato was, in some ways (not all) a fan of Sparta, something he got from questioning his world (that was why Socrates was sentenced to death), so he describes his ideal society as inspired by Sparta.
In Sparta, that was a Scandinavian city (descendants of the sea peoples that roamed the Mediterranean some thousand years before Christ), men and women were very equal. This tradition was something that Sparta had kept as a tradition all the way back from their founding.
In many ways, the Spartan society was a Viking society, men and women were not kept for a long time in family structures, and their children went to schools at an early age (that is the ideal behind our welthfare states, they are inspired by the Spartan agoge system.)
Plato was, as always, quite deep in his understanding of this system (Athenians are also descendants of the sea peoples, according to Wilhelm Gronbech), he philosophizes about this equality, and argues, that it creates harmony (the same idea that is behind progressive tax).
This point had really eluded Marx, who have never written about harmony in gender.
Marx was a quack in many ways, he had some good analysis, but his ideas are quite shallow. He does not understand the world he talks about, and he misses a lot of the basic points in the philosophies.
Anyway, equality has the aim of HARMONY. At the same time, Plato has a whole beautiful philosophy about love, so there is really no conflict between platonic love and equality in between men and women. Plato made up both ideas.
G-d bless the will to truly understand the theories behind the gender debate.