For a long time, I thought the answer to the question posed in the title of this piece was an unequivocal "No". This conviction was not lessened by Stephen King's assertion that:
"...while it is impossible to make a competent writer out of a bad writer, and while it is equally impossible to make a great writer out of a good one, it is possible, with lots of hard work, dedication, and timely help, to make a good writer out of a merely competent one. "
King, Stephen. On Writing (pp. 160-161). Hodder & Stoughton. Kindle Edition.
This assertion follows King's suggestion that writers form a sort of pyramid, with really terrible writers at the bottom, a smaller group of 'competent' writers on the next level up, even fewer 'good' writers, and a tiny number of geniuses like Shakespeare.
Let's unravel this a bit. In my experience, really dreadful writers don't know they cannot write. They are in that state of 'unconscious incompetence'. (For an explanation of the four stages of this model, see Conscious Competence Learning Model.)
What ought to happen is that as they get better at what they do, they move on to the next stage, that of 'conscious incompetence'. That is, they realise there is room for improvement.
The problem is -- and I realise I am vastly generalising here -- is that many of these people think they are brilliant already. (In fact, King's pyramid lacks a tier of people right at the bottom who have never written a thing in their lives but who are going to take the world by storm one of these days, ie when they have retired and have the time to sit down and write their book. Let's give the incompetent writers their due: at least they have actually roused themselves from the sofa and put pen to paper, so to speak.)
Where am I on the pyramid, and on which stage of the conscious incompetence model? The answer may sound contradictory, but perhaps you are in a similar position.
In terms of the pyramid, I believe myself to be at least on the 'good' tier. Perhaps, in my particular niche, I am even on the 'great' tier, or at least within touching distance. This declaration is not merely a matter of ego. Apart from the fact that many people (besides family and friends) over the years have said they really enjoy my writing, there are many magazines that have been willing, and are still willing, to pay me to write for them. If someone is prepared to offer cash when there are so many people around who are prepared to write for free (for 'exposure'), I must have something going for me.
However, as far as the consciousness-competence matrix is concerned, I very much regard myself as being consciously incompetent. This is not a question of false modesty: it is not an invitation to email me to say "No, no, you're wonderful" (though don't let me stop you!), but a matter of comparison. I read essays by David Foster Wallace, Gay Talese, Jorge Louis Borges, and feel that I still have much to learn.
After this long meandering detour, let's return to that question: can creative writing be taught?
Having done many writing courses at the City Lit in London, I have come to the conclusion that it can't. However, with a good tutor, anyone who has self-identified as consciously incompetent can make huge strides, and discover writing talent within themselves that was probably there all the time, but needed bringing out.
For me, the main benefit of the courses has been to be presented with opportunities to try out new things in a safe place, and to write in genres that I would never previously have considered. Also, to hear about, and have the chance to read extracts from, books I would not otherwise have discovered or tried.
I've come to the following conclusion. For a creative writing course to work, the student must be willing to learn from someone else, and the tutor must be willing to hold back from imposing their own way of writing.
In short, perhaps creative writing cannot be taught, but what can happen is that the conditions are established which will enable it to be learnt.