Littlemiss,
A good writing teacher should be able to provide exercises that will challenge and push his or her students to be creative. If all a writing teacher teaches is how to produce technically correct prose, they're not teaching writing. They're teaching grammar.
There are now countless university and college writing programs, and zillions of writing workshops out there. Some of these programs are very good, and some are not as good, but don't underestimate the ability of good instructors to motivate their students in the same manner a good athletic coach can motivate a sports team. A truly good writing instructor can get people to write things beyond what they considered their skill level to be, to write things they thought they couldn't. I've seen that done.
Yes, the basics of writing can be taught to people of at least average beginning ability. It's also not that hard to teach students exercises that will put them in touch with their own innate creativity. Which is not to say that every student in a given writing class will have the same level of ability. Some will be better than others, or produce better work, but that's true of any endeavor. It's also true, however, that the ones who may stick with it and eventually become published, may also be the ones whose work wasn't that polished in the beginning. That gets back to my point of how bad does someone actually want to be a professional writer? The ones with the most desire will eventually get there. I've seen that happen too, more than once. Simply because a writing teacher doesn't give you an A doesn't mean you're not any good. You might, if you keep with it, develop into a better writer than the teacher. Onwards...
One criticism I have of writing programs, however, is that some students can produce beautiful prose, poetry, non-fiction, screenplays, essays, etc., etc., as long as they are in a classroom or workshop setting, and as long as an instructor is making them do it. The minute you remove the instructor and tell them to go create good work on their own, many of them don't. They lose interest. The person who is going to become a professional writer ultimately doesn't need the coach. A coach or a classroom is there to give you a foundation and to get you started. Once you reach a certain level you either want to write or you don't. If you always need an external instructor to make you do it, you're not going to be a pro writer.
In regards to my own writing, once in awhile I still take a workshop. There's always somebody better who knows more about a given form or style than I do, or who can look at my work and suggest ways to improve it that I may not have thought of. Even if I reject such advice, it will probably force me to consider exactly why I've made some of the choices I have with my writing.
Well, those are my thoughts at the moment, best wishes, Terry