Sure, I believe myself to be a writer. In the context as a writer of my stories and the stories I collect from family. My teachers at university often commented that I wrote very well. That was after a lot of editing! I throw that all out the window with my memory journaling. It's very much freestyling.
This reminds me of my mother. She used to say, "I'm not a writer." Yet, she wrote letters. Lots and lots of letters. I'm lucky that she wrote many to me during the periods of time when she and I lived far away from each other. Probably about 20 years ago, I recognized that, while she didn't think she was a writer, her letters were beautiful, and her personality came alive through her words. I'd call that a writer. Thank goodness I kept every letter she wrote me. It's a legacy I'm grateful to have.