One reason could be that Dumbledore had too many other responsibilities in the wizarding world. He was the headmaster of Hogwarts and was constantly involved in dealing with the threat of Voldemort on a larger scale. He might not have been able to give Harry the individual attention and care that a true guardian should provide.
It could also be that the author wants to explore other relationships and character developments. By removing Dumbledore as Harry's guardian, new dynamics can be created. For instance, Harry can form stronger bonds with other characters who become his guardians, leading to different storylines and character growth for both Harry and those new guardians.
Perhaps Sirius Black could be Harry's magical guardian instead. In the original story, Sirius had a strong connection to Harry and a great desire to protect him. Even though Dumbledore was a major figure in Harry's life, Sirius was his godfather and had a natural claim to the role of guardian.
One possible reason could be that Dumbledore wants Harry to have a more normal upbringing away from the spotlight of Hogwarts and his own influence. So he deliberately steps back from the role of guardian.
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.
In some fanfics, Sirius Black could be an alternative guardian for Harry. Since Sirius was Harry's godfather, he had a strong claim to guardianship.
They probably have a very close relationship. Dumbledore would be like a father figure to Harry, guiding him through the wizarding world.
One reason could be to explore power imbalances. By making Harry seem like Dumbledore's pet, it shows how much power Dumbledore has over Harry's life and decisions. Another reason might be for a unique storytelling angle. It can create drama and tension, especially if Harry starts to rebel against this 'pet - like' status.
It could be that Harry finds out about Dumbledore's secrets regarding the Deathly Hallows. If Harry thinks Dumbledore was more interested in the Hallows for his own purposes rather than for the greater good, it might make him hate Dumbledore.
Maybe Dumbledore believes Harry isn't ready for the responsibilities that come with the lordship. Harry is still young and has a lot to learn about the wizarding world's politics and social structures. Dumbledore may want to protect Harry from making hasty or unwise decisions in a position of power.
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.
Maybe Dumbledore discovers some dark secret about Harry's past that he can't handle. It could also be that Dumbledore is trying to protect Harry in a really strange way, by pushing him away from the dangerous wizarding world around Hogwarts.