There's a tendency to think, I'm not a writer because:

I've never published anything

I've published a few stories, but not a collection

I published a collection, but not a novel

I published a novel, but from a small press

I published a novel, but my second novel didn't do well

My books are selling well, but I haven't been on the New York Times bestseller list

Rubbish!

If you write, you're a writer. The validation is in the words themselves not society's acknowledgement of them.