I recall a time in high school English class in which we studied "persuasive writing" or "argumentative writing." We were given a controversial topic--often something important like whether taking sodas out of vending machines would really stop childhood obesity--and then were required to write an essay arguing for or against.
I would argue--aha, you see what I did there--that everything we write is persuasive to a certain extent. Even descriptive writing can be persuasive.
I shall define at this moment, like a good English student, that "persuasive/argumentative writing" is not as linear as arguing for or against an idea but rather writing that tries to persuade the reader or make a point.
As a result, my statement that something like, "The light bulb in the room dimmed, then flickered, then went out," can be persuasive doesn't sound as silly. (See? That is why it is important to define your terms.) As a fiction writer, that statement is trying to persuade the reader that the room is spooky or what have you, depending on the context.
A story is persuasive because as an author, whether you do it consciously or subconsciously, you're trying to prove something to you reader. This is often interpreted as the theme of the story.
Therefore, a story is a vessel in which to try and convey your ideas to readers. Albeit a much gentler method than straight out debate, I think it is important as a write to understand the power each individual word/sentence/paragraph has. Each element is an example of persuasive writing and is working together toward describing a bigger idea, which is ultimately a piece of the writer's heart.