If you think about it though, you begin to realise that it's true. All writing is persuasive. This includes the obvious, which is politicized fiction that attempts to show the reader how the sociohistorical context used in the book influences the characters' choices, and, by extension, the reader's. I'm thinking here of novels like Herman Melville's Moby Dick, which include a long discourse on the sociopolitical ramifications of whaling, and The Octopus, by Frank Norris, which discusses conflict in California's wheat-growing regions between farmers, ranchers, the railroad, and the legal system. Another politicized novel is All the King's Men, by Robert Penn Warren, which foregrounds politics in the South during the dustbowl era, and the amoral rise to power of governor Willie Stark.
With sociopolitical novels, it is easy to argue that these stories attempt to persuade the reader to believe something in particular. Melville wanted to show the deplorable conditions for whalers, Norris hoped to bring awareness to the material deprivations of farmers, and the sacrifices they made, and Warren wanted to show how immoral and amoral politics is. Each writer's hope was that the reader would become motivated to complain and make changes, and in fact, each book is known to have had an effect on the readers of its time, which created material changes for the groups in question.
However, what about the novel Pride and Prejudice? Can it be said that Jane Austen attempts to persuade her reader of anything? Is she hoping for some kind of social change, or for her reader to think, feel, believe, or do anything in particular? Or did she write simply because she liked to write? I think that in fact, she did want the reader to understand something rather subtle. In essence, Austen's theme, throughout her six novels, is "unity." Think of the thing that the writer wants us to believe or feel, etc., as a concept or philosophy they're trying to "sell" us, the reader.
In Austen's case, she wants us to understand how very important certain Enlightenment values were to her. One of these values could be expressed through her plot device of the question of whether or not her characters would be married, and if so, would that person be a true friend? Friendship, integrity, moral standing---these were all important Enlightenment and Romantic era values, and Austen is indeed writing to persuade us of their importance.
You can tell a novelist wants us to believe something in particular when s/he uses certain kinds of language to express her values. It can also be seen through the subject matter she chooses to discuss. Textual evidence will support the novelist's theme, and language choices will indicate how s/he feels about the subject. Each sentence will be carefully chosen, whether consciously or not, to relay the novelist's values, and it is those values s/he is trying to convince you of.
The question is, will you agree or disagree with those values? That's when you find yourself nodding along to what you're reading, or perhaps rather vehemently saying "no." When that happens, you'll know the writer is trying to persuade you of something, and you're either in agreement or not, depending upon your values.