I don't think anyone can give a straight forward answer to that. Atleast not a simple one. I can't answer for everyone. I can only tell you why do I like to write. There have been times when I literally crave about writing something. I am in such a mode right now.
Anyways, I write because...
it gives me a sense of satisfaction
it gives me a sense of purpose
it gives an outlet to my emotions
it gives me an opportunity to check how well I can put my thoughts into words
it makes me feel alive
it makes me feel like a child again
it excites me
it intrigues me
I feel connected to words
I feel writing is the second most effective mode of communicating an idea after face-to-face conversations.
it helps me draft better :P (Yes, law students always think about drafting)
it helps me satisfy my unending urge to talk
it helps me think differently
it lets me know what people's opinion
it makes me feel like I'm giving something to the world which has taught me so much
But most importantly, I write because it makes me happy!
"Write from your heart, write from your soul. Make the best of your talent, and don't ever let it go. Not for anything."
Keep writing. :)