What does it mean to be a writer?
Sure, it means you get to drink an abnormal amount of coffee and call it a day, but it has to be more than that ... anyone can do that. Can anyone be a writer, though?
When I ask myself that question, I think of Remy from "Ratatouille," hanging onto the thought that "anyone can cook." Yes, anyone can do that. So, technically, anyone can write. But just because I can do a few math problems (and, trust me, a few would be the extent of it), I'm nowhere near being an engineer or mathematician.
Anyone can write, and many who hate writing are forced to attempt it in Freshman composition courses. However, just writing doesn't make someone a writer.
Like with anything in life, if you want to be a bona fide writer, you have to love it. It has to be where your thoughts wander when you're alone. It has to be the thing you use for comfort and, sometimes, a mode of escape.
Chances are, if you're not a "writer" you just thought about whatever your "thing" is. It could be anything: chemistry, dancing, computers. Everyone's loves and passions are different and lead us in different directions. That's what makes life interesting. Not everyone can be a writer, but that doesn't mean not everyone can write. I may not be a debater, but I can hold my own in any debate.
Honestly, no matter who you are, you can do whatever you want. The real clincher is in where your interests lie, because if we all liked the same things, we'd never learn new, important things.