It could be that Harry suspects Dumbledore of having ulterior motives and wants to confront him directly through a duel to get to the truth.
Perhaps Harry has been influenced by some external force or magic that makes him believe a duel with Dumbledore is necessary for a greater good.
Maybe Harry has a major disagreement with Dumbledore's decisions or strategies and thinks a duel is the only way to settle it.
I think there's one called 'The Wizard's Duel' where this happens. It's a really intense story.
I don't know of a particular fanfic with that exact plot. But you could check out some well-known Harry Potter fanfic authors and see if they have created such a story. Also, browse through fanfic communities and see if others have asked or discussed similar scenarios.
In some fanfics, Harry might hate Dumbledore because he feels Dumbledore has been using him all along as a tool to defeat Voldemort. Dumbledore has been making decisions for Harry without fully considering Harry's feelings and desires. For example, he didn't tell Harry about the prophecy until it was almost too late, and Harry might see this as a form of manipulation.
Maybe in the fanfic, Harry has his own ideas and beliefs that conflict with Dumbledore's. He might think Dumbledore's plans are too risky or not in line with his own sense of justice.
In some fanfictions, Dumbledore might bow out of respect for a powerful magical entity or a person with extraordinary abilities. It could also be a sign of his humility in the face of a situation where he realizes he is not the most knowledgeable or powerful.
Maybe Harry is under the influence of some dark magic or a powerful enemy who has tricked him. This enemy could have planted false memories in Harry's mind about Dumbledore. So, Harry, believing these false memories to be real, starts to expose Dumbledore as a villain based on these false recollections.
The power dynamic also shifts. Usually, Dumbledore is seen as a mentor and a figure of authority. But when Harry denounces him, Harry is challenging that authority. In some fanfic, this could lead to a power struggle within the wizarding community as others take sides. It can also cause Harry to seek new allies who share his view of Dumbledore, changing the social fabric of the story.
It could be because of a deep-seated grudge or misunderstanding. Maybe Harry felt betrayed by Dumbledore's actions or decisions.
Perhaps Harry was feeling betrayed or misunderstood and wanted to express his strong emotions directly to Dumbledore through a howler. This could be a way to make his point and demand a response.
It could be a very strange or creative statement. Maybe it implies that in some fictional or fan - created scenario, Dumbledore is involved in selling fanfiction related to Harry. But in the original 'Harry Potter' universe, this is completely uncanonical.