Wow! That is a great question. My first response was to think that it's because you can create any character that you want and do with them as you see fit. But, I can't say that's really true. I'm working on a book now where my female character refuses to be anything more than a very naïve twenty-something. I keep wanting her to be more mature, but she's fighting me. I just have to let her be who she is and deal with it.
So, I guess the best thing I like about being a writer is the element of surprise I enjoy as my story takes shape. I get to go along for the ride even though I'm the writer. Also, I love to meet new people in the form of my characters--even though they only live in my imagination, they still have their own distinct personalities and I like them. And finally, I love the way writing makes me feel: Happy!