Your wife wears the trousers has a completely different meaning in English, like she is in charge. Is it the same in Polish by any chance?
In fact it is the same. 'Nosić spodnie' when said about a woman means 'to fulfil a role stereotypically assigned to men'.
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.
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 :(