This is a blatant non sequitur. Counterexample:

It's hard in many places to be a male schoolteacher, because men are seen by parents and other staff as potential predators, to the point where some people won't even trust a man to change their kid's diapers. Men have said that this is a big reason they don't want to become schoolteachers, so if we help change public opinion on this front, then we've ostensibly lessened a gender imbalance without "forcing" any men to "change their desires."

You have to know that isn't true, which makes this a great example of why people are frustrated about discussing anything 'political' in the workplace.

If you see similar patterns across many different cultures, including ones considered to be more gender-egalitarian, I would have honestly thought the conclusion would be, in fact, varying interests.

Or do you think there are no biological differences (on average) between men and women, in which case, I can provide you with large, multi-national studies that come to a different conclusion.

I can see how there could be debate about how much the difference is, and what the causes of it are, but "you have to know that isn't true" seems like saying "Come on, everyone knows the world is flat, stop arguing in bad faith".

I know it is true, by looking at empirical data. Can you cite data that support your conclusion?