Leaders lead, cooks cook, writers write.
If you are a writer, you write. That you write well, that you write many words, that you write in a particular genre, or get paid is all description, detail after the fact. A writer writes, so to be a writer, you must write. The intent of the statement is not to ensure you understand you are not a writer if you don’t write. No, just the opposite, it is to validate you, so when people ask what you do, you can tell them confidently, “I’m a writer.”
Writing is not like doctoring or lawyering. No one will die or go to the electric chair if you lack skill. Those who want writers to hold a degree in English or a master’s in a science are, at the least, misguided, and at the most, elitist, who probably can’t tell an interesting bedtime story to their own children.
Now, to be fair, there are English teachers and scientists in the writer community. There are also doctors, lawyers, comedians, carpenters, and cooks. Regardless, no elbow patched blazers or cherry bowl pipes are needed (although I must confess, I always wanted one of those blazers). Nor is there any need to drink chamomile tea or buy a lonely cat. If you write, you are a writer.