He might think fanfic distorts the original concept.
One reason could be that Harry wants to maintain the purity of the original narrative. Fanfics can introduce all sorts of new ideas and directions that he may not agree with. Another aspect is that he might be trying to protect his own brand or the brand of the original work. Since fanfics are not always in line with the official vision, he may see them as a threat to the overall perception of the story or character.
Perhaps they fear that fanfiction could deviate too much from the original themes and values of the Harry Potter series. The official story has a certain moral and ethical framework, and fanfiction might distort it.
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.
It could be that the fanfic contains offensive content towards them or their fans. Thus, Barry and Deo join to refuse it.
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.
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.
The fanfiction could be presenting a version of Naruto that doesn't align with the canon. In the official Naruto story, he has a specific growth arc and personality traits. If the 'cra fanfiction' changes these too much, it's like creating a different character altogether. Naruto, as we know him from the original, would not be part of such a misrepresentation.
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.