I write entirely to find out what I'm thinking, what I'm looking at, what I see and what it means. What I want and what I fear.
You don't write because you want to say something, you write because you have something to say.
F Scott Fitzgerald
If there's a book you really want to read, but it hasn't been written yet, then you must write it.
See, these guys can't even agree on WHY to write--you think they're really going to agree on how? Don't fall into the trap of listening to these sophisticated-sounding quotes too much. They're nifty to think about, but you have to come up with your own whys, your own hows, your own whats, and your own magic. If you can't imagine not writing, if it stresses you out to go more than a couple of days without writing, if you wake up in the morning and go to bed at night thinking about writing, you should probably write. But more fundamentally, you should write if writing brings you joy, happiness, and pleasure (or at least a sweaty sense of "hurts good" catharsis).