> I can guarantee you that way more men applied to Caltech than women did.
You cannot guarantee that. Show some data or don't say anything.
> That means the most talented and impressive young man who applied and didn’t get in is objectively more talented and impressive than the least talented and impressive (though still extremely talented and impressive) woman who applied and got in.
This doesn't follow. If women self-censor (not sure how to say it in English correctly) their applications in such a way that only top women dare applying, while men don't, then no, it's not true that the men who didn't get in are more talented than the women who didn't get in. I'm not speaking in hypothetical, this is what actually happens - see e.g., Bosquet C., Combes P-P., García‐Peñalosa C., 2019, « Gender and Promotions: Evidence from Academic Economists in France », Scandinavian Journal of Economics, 121 (3), 1020-1053 or https://lejournal.cnrs.fr/nos-blogs/dialogues-economiques/pl...
The rest of your comment is based on faulty premises so I won't bother replying point by point.