We’re not trying to change minds with information. We’re trying to sway a moral ‘balance’ - these are people who know perfectly well that what they are saying is not true. They will only be persuaded to tell the truth when they feel the harm done by the lie outweighs the harm done by the truth.
Yes, those on the side of 'gender' are using emotive arguments*, not reasoning, evidence, stats, data, etc.
I find it interesting that most women are less inclined to talk about the emotive reasons they may have.
For example, many if not most women have experienced sexual assault at one time in their lives. But most don't wish to bring it up, maybe don't want to spell out the consequences. We hear an awful lot about how 'marginalised' some people are; not so much about how 'marginalised' women are. In fact, I don't know if I've heard that used, ever, as an argument.
*Which are of course largely anecdotal and unquantifiable, by their nature.