Here's the thing:
I think that anyone can be a writer, but that not everyone who has ideas and can assemble coherent sentences is a writer.
Good creative writing involves choosing just the right word for the moment, along with paying attention to the ways words and sentences come together and the effects that, together, they create.
In short, writing is a craft. That means that it's hard work, and a good portion of the time, it'll make you want to set yourself on fire and jump into a pool of gasoline.
But if you're a writer, you won't want to spend your time any other way.