There's a Land That I See; Or, The Spirit of Intervention
If you want to make your stupid dream real, you need to have a realistic picture of the world. If you want a society in which men and women have the same brain, or one in which feminism actually works, you would have to make it so, with advanced biological engineering. John Varley writes fiction: so did Joanna Russ.
We socially-liberal individualist/feminist people—I hope I'm still allowed to use the first person here, although the reader will ultimately judge that for herself—have this beautiful moral ideal, where we want all people to be free to maximize their potential, unencumbered by oppressive cultural institutions specifying roles and destinies in advance. We want everyone to be judged on her or his own merits rather than treated as a representative of their race or sex. We believe that if a trait is virtuous in a man, it has to be equally virtuous in a woman—as a matter of sheer logical consistency.
And because we care about the beautiful moral ideal, we tend to assume that psychological group differences don't exist, or are superficial, or are socially-constructed and will naturally dissipate after we muster the political will to achieve a more socially-just world.
(... the scintillating but ultimately untrue thought.)
But this is so crazy on multiple levels.
Firstly, philosophers since the days of D. Hume have recognized the distinction between is and ought, and have identified the naturalistic fallacy of direct inference from the former to the latter. That there exists a naturalistic explanation for the current state of affairs—and how could there not?—doesn't imply anything about that state being good or just or worthy of being preserved.
Secondly, not only does the nature vs. nurture dichotomy fail to hold up to basic scrutiny (the question has been compared to asking whether the area of a rectangle is caused more by its length or its width), it also isn't even adequate to the inferential work we tend to expect of it: not everything biological is immuatable, and not everything social is easy to change. (Consider the case of spelling reform: no one would suggest that the myriad quirks of English orthography are genetically determined, and yet the entirely social difficulties of getting everyone to coordinate on more logical spellings seem insurmountable.)
... you're going to have to bootstrap from today's, unremediated, genderspace. Which requires understanding it first.