As you are the one who disagrees or opposes the theory, then the onus to prove it wrong via peer-reviewed evidence is on you.
What, are you crazy? You proposed the theory — the onus is on you to prove it, or at least give some sort of evidence for it!
If I claimed that men and women’s brains differed (statistically) (a) in physiology, (b) in aptitude for various tasks, and (c) in preferences for e.g. risk-taking or work-vs.-family — you’d expect some data from me, wouldn’t you?
And in fact I do have the data for this (that study covers physiological differences and aptitude differences, but not risk-taking appetite, so here’s another one for that). TL;DR: significant statistical differences were found, but with lots of overlap on an individual-to-individual basis. Pretty much what casual observation would tell us to expect.
[And you can’t claim that “oh, it’s discrimination”. How would discrimination produce physiological differences? And those physiological differences were found to partially mediate the statistical differences in aptitude, thus linking aptitude difference directly to biology and not culture or “patriarchy” or whatever.]
Also, given how politically sensitive this kind of research is — investigating why men and women are represented differently in various professions — it’s rather rich of you to come demanding data. Your side is the one trying to prevent the data being collected by silencing anyone who suggests that maybe, just maybe, some of the inequality isn’t due to evil patriarchs or frat bros with their caps on backwards. [Perhaps you, personally, are against this kind of censorship — though it seems not from what you wrote so far — but nevertheless you ought to be aware of the barriers being created against such lines of inquiry.]
Your side already claimed the scalp of no less than Larry Summers for this — despite the fact that (a) he suggested only the possibility of this, (b) he cited studies to back up his suggestion, and (c) he expressed hope that he would be proved wrong. Didn’t matter, his head was still removed and stuck on a pike in the town square for all to see.
Don’t you think this would have a sort of chilling effect on the collection of data? And if so, why would it be that one side would act to bring about that effect?
