Well, trousers were originally for men, and it took some time before any women started to wear them instead of the previously and only used skirts and dresses. Blue jeans were an important step towards this direction. In Sweden though, I have not heard this phrase because it is one of the top countries in equality of genders.
Well, it creates quite a big grammar mistake, so I think it's good that a language-learning website rejects it. Sure, I guess most people that type it do it by mistake, and I also get annoyed by being marked wrong only by typos sometimes, but well... "wear" is simply wrong here.
Perhaps some wrong answer may still be accepted somewhere, but "to wear" is one of the few verbs that actually show a difference between Present Simple and Present Continuous. "nosić" is for Present Simple. The Present Continuous version is "mieć na sobie" (literally 'to have on oneself') and has somehow been forgotten in the process of creating this course :(