Here's my thing- it's my opinion, and as a writer I do have a valid one, this is akin to narrow-minded thinking. You are dismissing someone's potential because it doesn't meet your concept of what a writer is.
I speak from personal experience and I have many friends who have taken the route of self-publishing. Many are much happier with this decision than having gone with an agent / publishing house.
If you have the passion, the determination, and the fortitude to write- not to mention the imagination it takes- then become a writer. If it's all you can think about, not just the mechanics but the vision, that over-active imagination that creates countless characters and seemingly endless scenarios- then, my friend, take a shot at being a writer.
Don't worry about those people who tell you to give it up, that unless you're published you're not a writer. If you're self-published then you're not really published. These are the folk who- on the subject of your writing- first ask: "what have you published?" Then if you admit that you haven't been yet, they get a scowl on their face. Some are brazen enough to say "then you're not a writer." Sometimes I want to smack these people up the backside of their head (Gibbs smack) or pull a Stephanie Tanner- with a huff, saying "how rude."
Never let someone discount you because you have yet to see your work published or chose to go with self-publishing. If you have a story (or stories) to tell and you have been working on them- then you are a writer.
I mentioned earlier that I speak from experience. I have had several people in my lifetime tell me "you're not a writer" because I wasn't published or was considering self-publishing.
At this point, I have over 60 works in progress, have a counted 500,000+ words written among various projects- this includes novels, fan-fiction, fan-lit, blog posts, and academic papers. Writing is my passion, it's what drives me. There have been times when my imagination was in overdrive that I could not sleep until the muse was done with me.
No, I'm not published- YET. The day is coming and for the moment I'm undecided if I'll go with a publishing house, an agent, or self-publish. I just know that it will happen.
The day will come when people will walk by a major bookstore and see my book, or yours, or someone else's one of us knows - and we'll smile. Not because it's there but because we'll remember the asshole who said "you're not a writer."