The 'Harry Potter' series is not just about relationships in that sense. It's about magic, mystery, and heroism. Focusing on inappropriate relationships in fanfiction detracts from the more important themes of the story and the positive influence it can have on readers.
It goes against the canon. In the original 'Harry Potter' books, their relationship is clearly a deep friendship. Changing it to a sexual relationship in fanfiction is a misrepresentation.
One possible reason could be that Hermione sees Harry more as a friend. She has a deep, platonic bond with him and doesn't want to risk ruining that friendship by turning it into a romantic relationship. In the original story, they have been through so much together as comrades in the fight against Voldemort, and she may value that camaraderie above all else.
One possible reason could be that the writers lost interest in the Harry Potter fandom. Maybe they found other fandoms or stories more appealing.
In some fanfictions, there might be a new magical element or prophecy that makes Harry question Hermione's motives. If the prophecy says something about Hermione being involved in a dark plot, even if it's false, Harry may start to have doubts about her.
In fanfiction, Hermione's obsession with Harry could stem from her own insecurities. She may see Harry as someone who is more confident and free - spirited. She is obsessed with him as she wants to be part of his world, which seems more exciting compared to her own studious and rule - following nature. Additionally, their friendship has a strong foundation, and the writers of fanfiction might exaggerate this into an obsession to explore different storylines.
She can support him academically. Since Hermione is very studious, she can help Harry with his homework, prepare him for exams, and share her vast knowledge of magic. This not only helps Harry in his studies but also boosts his confidence.
Maybe it's about her study habits. For example, she always preaches about everyone following the rules in class and doing their homework properly. But then she might break a minor rule herself when it comes to getting access to a certain book in the library for her research.
One possible reason could be a misinterpretation of their relationships. Maybe the author wants to explore a different dynamic where Harry and Hermione bond over Ron's perceived flaws, like his occasional laziness or his insecurities that might come across as annoying to them in this fictional scenario.
One possible reason could be that Hermione might be too overbearing in her studies and constantly nags Harry about his schoolwork in the fanfiction. This could annoy Harry and make him mad.
One possible reason could be their different career paths. Harry might be more focused on Auror work which is dangerous, and Hermione, being the practical person she is, may not want to live in constant fear for his safety. Another reason could be a growing apart in their values. Maybe as they get older, Hermione realizes that Harry has a more impulsive nature when it comes to making decisions regarding the wizarding world's politics, while she prefers a more calculated approach.
One reason could be to start anew. After all the turmoil in the British wizarding world, they might want a fresh start away from the memories. The USA offers a different magical landscape with new opportunities.