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.
It could be that Harry has been misled by some false information in the fanfic. He may believe that Dumbledore is hiding something bad from him, so he refuses to listen. For example, if there are rumors about Dumbledore's past actions that make Harry doubt him, it would lead to this situation.
In the fanfic, Harry might be in a situation where he has grown independent and wants to make his own decisions. He has experienced a lot and feels that he can no longer blindly follow Dumbledore. He might think that Dumbledore's way of dealing with things is too old - fashioned or not suitable for the current complex situation. He wants to explore his own path to solve problems, rather than relying on Dumbledore's instructions all the time.
Maybe he has his own personal reasons. He could be afraid of failure, or perhaps he doesn't like the competitive environment. Another possibility is that he has some moral objections to the nature of the competition in the fanfic.
There could be ethical reasons. Fanfic sometimes involves using characters and settings created by others without proper authorization in a more complex way than just being inspired. Harry might not want to get involved in teaching something that has such potential legal and ethical gray areas.
Maybe he has his own reasons. He might be tired of the responsibilities that come with being a hero. In the fanfic, perhaps he has seen the dark side of heroism, like the constant danger and the loss of personal freedom. He could also be a complex character who doesn't conform to the typical heroic image.
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 he has his own principles. In some fanfics, Harry might have a different view of SHIELD's methods or goals. He could be more of a lone wolf type and doesn't want to be part of a large organization like SHIELD.
Maybe in the fanfic, Harry has some unresolved personal issues. He could be haunted by his past traumas, like the death of his parents and his battles with Voldemort, which make him feel that he's not in the right mental state to get married.
Maybe Harry has a major disagreement with Dumbledore's decisions or strategies and thinks a duel is the only way to settle it.
He might think fanfic distorts the original concept.
Maybe he has a very traditional view on literature. He might prefer to stick to the original works and not engage with the fan - created versions. Fanfiction often takes the original story in different directions which he may not like.
One possible consequence is that Harry could put himself in danger. Dumbledore is usually very wise, and his advice is often meant to protect Harry. By not listening, Harry may walk into a trap or face a more difficult situation than he expected.