You can't "teach" composition. You have to learn through experience. Studying under another composer is really the only way to be "taught" how to be a better composer, the rest is just trial, error, and experience. But even then, all I ever did in my composition courses was bring in what I was working on, and have the teacher look at it. He'd say "this is good" or "this part's confusing, I'm not sure what you were trying to say, here," or "this reminds me of _____, you should read this book/watch this movie for some extra inspiration" and stuff like that. And that was immensely helpful for me.
It's not like you sit down and be like "okay, write a string quartet. Go!"
Things you can teach: Theory and Orchestration.