Thinking of Myself as a Writer

I was all prepared today to talk about my day yesterday and how my classes went. They went well. But there was so much more than just sitting in a chair and listening to a lecture. The thing that really struck me the most was when our professor (and my interim adviser) told us that we need to change our perception of why we are in Grad School. We have to think of this as our time to work on our writing, because he said, we are all writers and just improving our craft. I have never considered myself a writer. I've always been defined by what I did for a living, and certainly writing in Grad School isn't paying my bills. Have I got it all wrong? Should we be defined by our passions and interests? Or should we be solely defined by what pays our bills?