Game design or Game art

I disagree that game design can't be taught; having said that, I haven't heard of any courses that do so well. Like any form of design, game design is about crafting the experience your end user will have with your product, anticipating what their reactions will be, and tailoring it to evoke the desired reactions and emotions from the player/s.
You don't need original ideas, or terribly much creativity to do this, although both help immensely. It involves thinking about what kind of experiences you want your players to have, and then designing mechanisms through which they can encounter them - and that is, I believe, something that can be taught.

Agreed. I am in the firm belief that anything can be taught, but it is more of an easier learning experience for certain individuals that are talented.

I agree with this as well.

Me too.