I found this while I was considering your conundrum:
"Why do writers write? Because it isn't there." - Thomas Berger
I heard one person suggest that defining a writer is as simple as asking, "What makes an electrician an electrician?" In this line of thinking, an electrician is someone who installs electrical devices and wiring. A writer then is someone who writes.
If this definition is true then you are not a writer if...
1) You have a major in journalism, but do not use your skills.
2) You only wait to write if there is a reason to write. In effect you will only write if a publisher asks for an article.
3) You dream of writing someday, just not today.
I don't know if this if an absolutely perfect definition of a writer, but the truth that 'writers write' is sometimes lost on individuals who have the skills to write, but rarely do.
Around the world there are individuals today who will sit down and map out a story, they will craft a sentence, they will dangle a few participles and some may finish a story they've been working on for months.
These tenacious individuals sit down each day to write. They may not be published yet, but they have already accepted the mantle of 'writer' simply because they have given themselves to the art of writing.
"Get it down. Take chances. It may be bad, but it's the only way you can do anything really good." - William Faulkner
It's possible to have a writing career, but you must first ask yourself if, in fact, you are a writer.
I don't want to belabor the point, but if you have the skills to write and refuse to use them you may not be a writer. This point is made by looking at a person who has gone to electrical engineering school yet refuses to actually work with electricity.
I am well aware that the notion of defining a writer is broad and often vague. It is also a point that can be argued ad infinitum, but the purpose of this article is to encourage those who are dedicating themselves to the craft of writing. Each day you are learning more about yourself and how you define the world around you. With each pen stroke you are creating new worlds or explaining old ones. With each stoke of the key you are answering questions or creating new ones to consider.
If you simply must write today, as you did yesterday, last week and last year - you are a writer.
"If you write one story, it may be bad; if you write a hundred, you have the odds in your favor." - Edgar Rice Burroughs