There is a difference between writing and being a writer. Having the ability to put pen to paper does not immediately make you a writer, because there's something more to it than that. The urge . . . no . . . the need to tell stories, the need to put a piece of yourself in your work, makes you a writer. Being a writer is an identity. It's a way of life.
"If you do not breathe through writing, if you do not cry out in writing, or sing in writing, then don’t write, because our culture has no use for it."
You can always tell when something was written by someone who didn't put their all into creating it. You know when someone's passion, their heart, isn't in the work you're reading. There's a spark missing. An intangible thing that is nevertheless noticeable in its absence. A person may try to write stories merely to make money or make a name for themselves (though there are plenty of more profitable professions to pursue if you don't mind only being in it for the money), but the work will inevitably suffer for it.
Why should we even care about this? Some would say a novel is just fiction. How could it possibly matter?
"One can be absolutely truthful and sincere even though admittedly the most outrageous liar. Fiction and invention are of the very fabric of life."
Fiction can offer us the things that real life may not. We can experience cultures we've never been a part of, find ourselves in social situations we never previously imagined. If an author is sincere in their creative passion, they can help provide us with a rich tapestry of experience we never knew we were missing until we found it.
A creative work, when filled with passion and commitment on the part of the creator, is so much more than mere words on the page. It has the ability to reach people, to transform people while providing new perspectives and/or provoking strong and meaningful emotions. We all have those stories, those characters, that we carry with us forever. To create something this powerful and enduring, you need to put everything into your writing.
If you can put that kind of dedication into your work, then you are a writer. Even if you're unpublished, that does not alter the fact that you are a writer. Be proud of that fact, and don't let anyone tell you that you can't do it. The potential to do great things is always there as long as you're willing to put everything you have into doing it.