Dom Casmurro wants understanding from the reader—and to convince himself that he deserves that same understanding. He's a lonely old man who is unable to recapture the joy of his youth. He tries several different ways to do so, including recreating a house he once lived in. Ultimately, though, these attempts fail. At this point, he explains, he decides to write a book but can't decide what to write about. Then he realizes that he might be able to recapture his youth by sharing the story of it.
Taking a step back and feeling younger isn't the only thing the man wants, however. He wants to absolve himself of guilt by sharing his story with the reader. Throughout the text, he tells them that what he's saying is true, that they can put down the book if they're bored, to shake their heads if they don't believe him. He coaxes and convinces them to see things from his point of view. It's almost as if he believes that if he convinces the reader, he can convince himself.
Casmurro—whose real name is Bento—isn't the most reliable narrator, however. It's up to each reader to decide whether they believe in his allegations about Capitu's fidelity. Ultimately, no matter who is at fault, Bento is alone and left to argue in the pages of his own book.