Well, it could show that their relationship was based on false pretenses. Harry might find out that Dumbledore had ulterior motives for taking him under his wing. In the fanfiction, this would completely change the dynamic. Instead of the warm, if somewhat distant, relationship in the books, it could be a relationship where Harry feels used and deceived. This new view of the relationship would likely drive Harry to break away from Dumbledore's influence and forge his own path more determinedly.
One possible reason could be Dumbledore's over - reliance on his own grand plan. He might have been so focused on the big picture of defeating Voldemort that he overlooked Harry's individual emotional and psychological needs. For example, Harry constantly had to face dangerous situations alone, and Dumbledore didn't always step in to protect him directly. This could have led to Harry feeling abandoned and having to grow up too fast without proper guidance in some aspects.
One possible reason could be Dumbledore's over - reliance on his grand plans. He might have been so focused on the big picture of defeating Voldemort that he overlooked Harry's immediate emotional and mental needs. For example, Harry had to face many traumas alone, like the death of Sirius, and Dumbledore didn't always provide the support Harry really needed at those crucial moments.
It can create a lot of angst and drama. Harry may become more distrustful of authority figures, which can lead to him making decisions on his own that are either very good or very bad. For example, he might go off on his own to fight Voldemort without proper backup because he doesn't trust Dumbledore's plans anymore.
Dumbledore, as Harry's guardian in the fanfiction, would probably use his influence in the wizarding world. He could make sure that Harry is taught by the best teachers at Hogwarts. He'd also be there to offer advice and guidance, especially when Harry faces challenges like dealing with Voldemort or other dark forces. For example, he might teach Harry some advanced defensive magic privately to better protect himself.
Well, in some fanfictions, Harry might attack Dumbledore if he discovers that Dumbledore has been using him as a pawn in a bigger game all along. This feeling of betrayal could drive him to lash out. Also, if there is a prophecy that he misinterprets to mean Dumbledore is a threat to his future or the future of his friends, that could be a motive.
Snape can be a prominent character. Given his complex relationship with Dumbledore and Harry, his perspective could add a lot to the story. He might have some insights into Dumbledore's actions that Harry doesn't know about, and his reactions to Harry's blaming could vary from being scornful to having a moment of understanding. Luna Lovegood could also be a part of it. Her unique view of the world might make her offer some different viewpoints on the situation between Harry and Dumbledore.
Dumbledore might give Harry advanced spellcasting training. He could teach Harry some of the more complex and ancient spells that are not commonly taught at Hogwarts.
Hermione could be a main character. She might use her vast knowledge to help Harry and Dumbledore in their adventures. For example, she could research ancient spells or potions that are crucial for their mission.
Perhaps there are safety concerns for the students that Dumbledore is not addressing adequately. Harry, having a strong sense of responsibility for his fellow students, may feel that the only way to ensure their safety is to remove Dumbledore from his position. He might believe that Dumbledore's actions or inactions are putting the students at risk, and thus he takes matters into his own hands.