One seldom hears this question asked about other subjects. The answer is too obvious. Can painting be taught? Of course; indeed, any college can outline a sequence of disciplines that must be mastered to learn the craft. Can physics be taught? Sure—and it’s hard to imagine learning much of it all on your own. Music, which seems to me to rely heavily on inborn gifts, gets taught every day; I’m given to understand that this is what music teachers engage in.
Yet it isn’t uncommon for people (often professors of English) to claim that writing can’t be taught. I’ve often wondered why one hears this so much. Sometimes it may be a matter of envy (“I have to publish refereed papers on the use of images of illness in the works of Virginia Woolf—and Williams, over in Creative Writing, all he has to do is comment on a few student short stories!”) or self-justification (“I tried to learn to write, but I never made it as a writer—clearly it can’t be taught!”). But more often I think it's a result of unrealistic expectations.
Very few physics students, even those who do quite well on their exams, end up as brilliant researchers. Few dancers, even though they know every move and transition, become principals at the Met. Few musicians, even those trained by the best, make a living at performance or composition. Rising to the top of a field requires not only training and discipline, but talent and luck as well. Yet no one argues that because talent and luck are needed for a brilliant career that physics or dance or music can’t be taught.
One of the problems, though, is that so much of the learning of writing is self-teaching—self-teaching through years of reading, self-teaching through writing and failing. Musicians face the same sort of long self-education, listening to music in all spare moments, exploring different kinds of musical forms, and devoting hours to practice. I don’t know any good writers who aren’t lifelong voracious readers (though I’ve met plenty of people who don’t read much, but think they’d like to write), and most good writers I've known have long been serious spare-time scribblers.
When a student who has been a lifelong reader walks into a writing class, she is likely to have a subconscious grasp (perhaps a firm grasp, perhaps one that is a bit more slippery) of elements like rhythm, diction, pacing, and characterization. Often the teachers and other students respond by calling her ‘talented.’ And this student may well be ‘talented’—but much of her skill quite likely comes from sheer obsession, from years spent swimming in a sea of words.
Can writing be taught? Sure. But it's easiest taught to those who have already spent years teaching themselves. There's nothing mysterious about that.