I s2g men are incapable of seeing anything from women’s perspective unless you lay it right out flat in front of them, and sometimes not even then. They really act like we don’t even have feelings, and when we do, we’re being “hysterical” or “Karens” (which, I’m kind of amazed he didn’t have a comeback for you). It’s like they’re incapable of imagining women are human like them instead of objects to use for sex or domestic or emotional labor or just to laugh at and mock.
It was pre-widespread "Karen" usage in the immediate aftermath of metoo before the backlash really got going, and he was a professional proto-wokie (actually had a direct hand in TRAs getting their foot in the door to women's spaces). Also the right smartass tone in delivery and keeping the response short helped I think. Paraphrasing, was something like "So what you're saying is gay men are the ones who get to determine which men get to dress up as caricatures of women?" and left it at that.
Years ago I managed to shut down an idiot boss who was getting very indignant about an annual local drag show put on by straight men (usually in frumpy goodwill clothing, focus is on seeing local big names looking silly in ill-fitting dresses, kept very PG, done to raise money at Christmas for charity). He was complaining about straight men appropriating gay male culture...to a group of women. I pointed that out to him and it took the wind out of his sails a bit.