I am a self-taught composer, assuming the definition is merely that one has had no formal lessons with a teacher of composition. I’m certainly not a self-taught musician.
I attended the Manhattan School of Music as a pianist. I studied with Seymour Lipkin, a marvelous musician, and soon after, I met Paul Jacobs, who was a great help and inspiration to me. I had the requisite harmony and counterpoint classes at school, but I really learned to write music by playing it. Lots of it.
The very act of learning to play a piece of music is to re-think it with the composer, retrace his footsteps (finger-steps) and then in the best performances, re-compose it onstage. In this sense, I will always be studying composition. The obvious advantage for a composer in being a performer is that you can champion your music yourself. But it also makes networking easier: I find myself on stage with many wonderful musicians who are looking for new repertoire.