I would just like to say, that this is by no means a comprehensive explanation for every writer out there as we are all unique and creative individuals, but why we write tends to be a common theme among many of the writers I know... and for those of you who have a picture of a tortured artist numbing themselves to the world with copious amounts of narcotics, kick that out right here. I only knew one "tortured artist" and he wasn't really that good! (Probably why he was so tortured.) No, most of us who write are not tortured souls. We don't even feel more than others, despite that common misconception. No, I think most of us simply are able to express our feelings with words more easily than others.
I think that is why we write, as a means for expression. We who write love the words and the ability to shape feelings and thoughts in such a manner that others can relate. If we felt more than other people felt, then they could not relate to our writing. But our ability to express those feelings that others feel, but are not able to express themselves is what makes us unique and is what makes people read what we write. Even though they might not express themselves the way we do, they can relate to our expression and that is what makes it real for them.
Another reason we write is to share. Most writers don't write because they desire fame, fortune and notoriety (although few of us would snub our nose at it!) Most of us write to share. We want to enrich the world with new ideas and concepts. We feel a passion for our stories or perspectives and we want to show others that, much in the way that new parents show off their kids. We create through a labor of love for the material and the characters and we want the world to meet our characters and feel the same way we do. I think this is why many writers have a hard time with negative reviews. I mean, how would you feel if someone called your kid ugly? And our books are our children. We spend so much time and energy making them, expecting little monetary reward in the end. (Sounds like parenting to me!!) And it is just as fulfilling as parenting too as any writer who is a parent can attest.
I can honestly say, and most writers would agree, that even if I knew my writing would never be published and I would never get paid, I could never stop writing. Sure, it is nice to receive some modest compensation for what I have done, but it is so much more rewarding to see someone smile, or tell me that they love my character, or that they were not expecting that wild twist. I don't write for the paycheck, I write to relate to others. Although I will (probably) never have a lot of money, I will be far richer for the difference I have made in others lives.
That is why we write.