There's a story about a young writer who approaches an older, more experienced author with a manuscript, and asks, "I'm trying to make up my mind what to do with my life. Do you think I have what it takes to be an author?" The other writer skims over the manuscript, hands it back and says, "Forget it, kid. You don't have what it takes." The young writer goes away discouraged. The older author's friend is standing at his side and asks, "Why did you tell that kid he wouldn't make it? You barely looked at his story." "He said he had to make up his mind," the author said. "If he were really a writer, his mind would be made up for him."
There're probably authors out there who "back into" writing, discover they have a "knack" for it, but I've never met one. Writers I know take joy in it, but they also find it difficult and frustrating, and yet they keep at it. In conversations with writers I know, I always hear the same thing. They write because they have to; if they're not writing they're sick with themselves. Writers who are lying fallow become snarky and passive-aggressive; we nurse petty grievances and mutter under our breath. We have difficulty sleeping at night and getting up in the morning. This behavior indicates writing is an addiction, and withdrawing from it comes with symptoms not unlike withdrawing from any drug.
"Am I a writer?" The question is like asking am I a crack head. If you write, you're a writer. If you use crack, you're a crack head. Either way, if you shouldn't have to ask.