Sexism in NFL's Bag Policies

I went to an Eagles game last week (I know, I know, very off-brand) and my friend wasn't allowed to bring her bag into the game. She was forced to pay $15 to drop off her bag in a locker before we could get into the stadium.

A few drinks later we were discussing the obvious sexism inherent in the NFL bag rules. I understand that it takes more time to go through bags, and I am no security expert, but I would think that going through a metal detector would just solve all that? Can the metal detectors that you walk through at the stadiums not see through bags? Now that I'm really thinking about it, why don't bags go through the metal detectors with us at games?

The Linc has this on their website: Lincoln Financial Field has a clear bag policy. Guests are permitted to carry either one (1) clear bag that does not exceed 12' x 6' x 12' or small clutch bags, approximately the size of a hand but not larger than 4.5" x 6.5".

I have to add the Steelers requirements here because they are bit extra:

What's with the logo rule? You can't be an influencer? In all seriousness, the plastic freezer bag isn't a horrible idea...

Anyway, what my friends and I were discussing after the bag removal incident of 2021 was that this rule seems to only affect women. Let's say for example men's khaki shorts. You are telling me that men's khaki shorts don't have pockets bigger than 4.5" x 6.5"?? I'm just saying if we can't carry a purse bigger than that, men shouldn't be able to have pockets that size. I'm not trying to sound like this lady and heaven forbid I don't allow the men of Western Pennsylvania to wear khaki shorts, but it just comes across as a weird, one-sided rule.

We also went to a Phillies game last night, where we were all allowed to bring in a much larger bag, so I am once again simply puzzled by the NFL's stricter rules. Are the metal detectors higher quality at MLB games? Anyway, here we are on TV with our bags: