Belatedly, and just for the record, I must admit that my first response in #2 was, to say the least, incomplete. Helen (#8), you're quite right in pointing out that my second example should have been in the continuous tense, I was concentrating on the infinitives (to play guitar/to play the guitar), so please forgive me. What is more important is that you think the article is optional. When I read hm--us's examples in #9 I found they all sounded fine to me, and I tend to take your point of view.
I guess that I tried to re-read the teacher's mind and, concentrating on the obvious mistake in the initial query (a misplaced 'the' in the reported teacher's reply), overstretched the argument somewhat. Apparently, the teacher wants to make a distinction between 'playing guitar' and 'playing the guitar'. I actually thought I could argue in favour of a distinction, too, but I stand corrected.
"I play guitar -- A, D, E --
I don't play bass, 'cause that's too hard for me,
I play the piano if it's in C..." (Britpop 1970).
Thanks to Helen and hm--us for correcting my rash reply.