No need to lose it over a simple Duolingo sentence and declare it sexist. I'm sure you wouldn't care about a sentence like Männer mögen Autos (men like cars), so why this one? It's certainly somewhat of a generalization, but all in all it is more often than not true to a certain extent.
You're probably joking, but if you're not then you really need to take things a bit less seriously, this is just a randomly generated Duolingo sentence. Just because men tend to like cars doesn't mean women aren't allowed to take care of their cars, I really don't get your logic (or satire, I can't even tell).
The word doesn't change in the plural, like all diminutive words (-chen and -lein). You can know it's in the plural because:
- There is no article (girl like[s] shoes wouldn't make sense unless plural in English, too)
- The verb is conjugated for the 3rd person plural (ich mag, du magst, er/sie/es mag, wir mögen, ihr mögt, sie mögen).