Here's the text of Notes from Underground from Project Gutenberg.
Let's skip the infamous first few lines ("I am a sick man. I am a spiteful man") and perhaps return to them later. And let's approach the infamous narrator who utters them, the Underground Man, from a different angle--his addressees, whom he calls "gentlemen." For instance, here's a short passage from Part I:
You imagine no doubt, gentlemen, that I want to amuse you. You are mistaken in that, too. I am by no means such a mirthful person as you imagine, or as you may imagine; however, irritated by all this babble (and I feel that you are irritated) you think fit to ask me who I am--then my answer is, I am a collegiate assessor.
When I've taught this book in Comp Lit courses, I've seen students get quite irritated indeed by lines like these. Their reaction is something akin to what many of us feel reading stories in the dreaded second-person, to wit: "You are riding on the subway..." No, I'm not, you idiot.* The students say things like: How dare the Underground Man (or is it Dostoevsky?) assume I'm irritated? OK, I am irritated, but not for the reasons he thinks. He's putting words in my mouth; that's why I'm irritated. (Also, some will point out, we're not gentlemen.) And they read the rest of the book with a nice big chip on their shoulders.
But what if Dostoevsky, and the Underground Man, want us to read with that chip? Let's assume the UM knows we think he's misread us, and that we'll therefore resist what he has to say. What might be Dostoevsky's purposes in doing that? And how does that affect the narration?
So here's a writing experiment: creating a reader--to whom you explicitly refer in your story--whom your narrator deliberately, strategically misunderstands. This should go beyond the exercise of, say, writing a letter to a hostile or skeptical recipient. Your narrator is toying with the real reader by creating a sham version of that reader--a kind of voodoo doll that the narrator pokes to get a reaction out of the unseen person it represents. What strategies would you use for poking? Why and how do you want the reader to resist?
*By the way I have written a story in the second person. But I expect a fair number of people to loathe it.