"What would you say to someone who was very interested in cartooning, but gets regularly criticized by art teachers for doing so? Just to do what comes naturally, or should they try out other styles?"
I suppose what your professors want from you is to be able to be polyvalent on everything (which is something that an artist should do, even if that artist has stronger points on things than others)
From your gallery, it seems you have a nice style but absolutely no fundementals (such as anatomy, perspective, composition, etc...) present on your works, which also may be the reason why your professors are criticizing you.
[link] which contain books/blogs for artistic improvement.
It doesn't mean you have to drop your comic style completely, but you need to learn these fundementals to increase the quality of your works, to make them more varied, and also to make your actual style more appealing and better (though nobody would fault you if you have a change of heart in what style to pursue after learning everything from Loomis/Villpu/etc...)
also
>asking advice from "mediocre" artist Preston
damn girl