One possible reason could be that in the fanfic, Harry discovers Snape's deeper motives earlier. Maybe he stumbles upon Snape's memories or has a series of interactions that show Snape's true loyalty to Dumbledore and his complex role in protecting Harry all along. This new understanding makes Harry admire Snape.
Perhaps in the fanfic, Snape is portrayed as having a more empathetic side towards Harry. He might show kindness or give Harry crucial advice in a way that the original books didn't. For example, Snape could be the one to help Harry with a particularly difficult spell, and through this, Harry starts to admire him.
The development could also be due to the way the author writes Snape's backstory in the fanfic. If the author delves deeper into Snape's past, his difficult childhood, and his love for Harry's mother, Harry might start to understand Snape better. This understanding leads to admiration as Harry realizes that Snape is not just the strict and seemingly cruel professor he thought he was.
Maybe Snape wants to train Harry better. By using potions to change Harry's abilities or characteristics, he can expose Harry to different challenges and make him a stronger wizard. For instance, if he gives Harry a potion that temporarily takes away his ability to use magic, Harry will have to learn to rely on other skills.
One possible reason could be Snape's unfair treatment of Harry and his friends. Snape often showed blatant favoritism towards Slytherin students and was overly harsh on Gryffindors, especially Harry. This constant bias could lead Harry to want him fired. Another reason might be Snape's connection to the Dark Arts. Harry, having faced Voldemort, might be worried about Snape's knowledge and use of dark magic within Hogwarts. Also, Snape's generally unpleasant demeanor towards students could be a factor. His sarcastic remarks and cold attitude might make Harry think that he is not a suitable teacher for Hogwarts students.
One possible reason could be copyright infringement. If the fanfiction uses too much of the original 'Harry Potter' material without proper authorization, J.K. Rowling (or those in charge of the franchise) might take legal action. Another reason could be if the fanfiction misrepresents the characters in a way that goes against the intended spirit of the original work.
One reason could be to escape danger. Maybe Hogwarts is facing a new and extremely powerful dark threat that even Dumbledore can't fully protect the students from. Another reason might be for a unique educational opportunity. There could be a school in another part of the wizarding world that offers a specialized curriculum in, say, ancient magic or magical creature training that Harry is interested in. Also, it could be due to a conflict with certain students or teachers at Hogwarts. If there are people constantly causing trouble for Harry, he might consider changing schools to have a more peaceful learning environment.
One reason could be that he wants to escape the constant danger at Hogwarts. Maybe he feels that Voldemort's influence is too strong there and he needs a fresh start. Another possibility is that he has a falling - out with some of the teachers or students, and he decides that a new school environment would be better for him.
Their relationship could change if Harry realizes during the duel that Snape has been protecting him all along. This newfound knowledge could turn Harry's hatred or suspicion into respect.
Perhaps in this fanfiction, Snape shows a side of himself that is completely different from what Harry has known. He might be more open and honest with Harry, sharing secrets that make Harry believe he can be trusted. Like Snape might disclose some long - held information about Harry's parents that only he knew, which makes Harry think Snape has been on his side all along.
Maybe Harry Potter is tired of the unrealistic portrayals of Snape in fanfiction. Often fanfictions can exaggerate characters' traits, and Harry, who knew Snape in real life, might find these interpretations too far - fetched.
Perhaps Harry has a hunch that Snape is involved in some secret project or fight against the dark forces that requires basilisk parts. Harry, being the hero he is, decides to provide Snape with the parts to aid in this unspoken cause. It could also be a sign of Harry's growing maturity and his ability to see beyond their past differences.