You are what you do.
A writer is someone who writes. A lot. Every day. If you don't write every chance you get, you are not a writer.
If you have never performed in a play or on a screen, you are not an actor. You are probably a barista.
I am not a writer. I am a manic creative who occasionally writes. Some of my writing appears on this and other blogs. Sometimes I get published, which surprised the hell out of me, because I never do a second draft of anything.
A lot of the people I know define themselves by something they don't do. "I'm a musician" whose guitar gathers dust in a corner. "I'm an actor" who hasn't been on stage since high school. "I'm a Christian" who doesn't recognize quotes from the bible.
I do a little of a lot of things. I'm not any of them other than manically creative.