I write as a way of learning more about myself and the world around me. I write as witness, or in response to others' witness. I write because I have something to say, something to feel, something to sort through. I write because I want others to think about things in ways they've not previously thought. I write because I can't *not* do it.
I write fiction because I have a story to tell, as well as a truth. The idea for the story always comes to me in the form of a what-if, and it never comes when I'm looking for it. As for truth, I'm usually not conscious of that until the character(s) reveals it to me. And sometimes that can be well into the revision process. And before it's revealed, it's manipulated, denied, explored, hidden, questioned, argued, etc.
(A side note. I used to never get when lit professors talked about "hidden meanings" until I started writing fiction. And keep in mind that I was not a lit major in college, and my graduate work was in rhetoric. I don't think of my fiction as literary -- I think of it as rhetorical. I use symbolism. But sometimes that symbolism is lost on me until I read the final draft and say, "hey, neat." Or a reader finds something that had never even occurred to me.)
And yet, I also write fiction because it gives me a chance to re-arrange certain truths. After a disappointing outcome of a relationship, I wrote a novel (actualy, pieces of it -- I haven't finished it and may never do so, although my friend thinks it should be an HBO sitcom), and gave the protag the relationship I had wanted w/ this guy. I found it immensely satisfying to change the outcome. In a fictional world, the Twin Towers can stand tall again, or the Dodgers can remain in Brooklyn, or Jed Bartlett is president of the United States. I enjoy the Land of Make Believe. It was my favorite part of Mr. Rogers' Neighborhood. In rhetoric, the goal is to persuade. (I also loved when Stephen Colbert coined "truthiness." I've proposed academic conference papers on the subject, and have yet to be accepted.)
I also had lots of imaginary friends as a kid. How's that for truth.
That being said, however, I don't really get into fantasy or science fiction genres. Maybe it's too much belief for me to suspend.
Not to say that it's always easy; but in the end, writing is home to me.
I promise you that Aaron's answer was far less wordy and far more interesting.
And so, I pass the question on to you: Why do you write?