I think I stumbled across an answer to this just a few hours ago, actually. Obviously, this answer is specific to me, and may or may not change in the future, but... I think the reason I have musical impulses (even though I've never really been a songwriter, as such) is because there's an emotion inside of me that most encapsulates who I am, and this emotion has, to the best of my knowledge, never been fully expressed in music (or writing for that matter, hence being a musician and writer). So yeah... It's an internal desire to express something that I have never had the pleasure of seeing outside of myself, and music (and writing) seem to be the best candidates for how to do that.
Ack, that sounds kind of pretentious... I guess another way of saying it is that I think everybody is an individual on the inside, regardless of their external circumstances, and that for me, at this point, expressing that causes me to want to write and/or make music.