Hermione might go with him. She's always been by Harry's side, and she would likely follow him out of loyalty and also because she might see the value in whatever mission or journey Harry is embarking on. She could provide the intellectual support and research skills that Harry needs.
One possibility is that Harry leaves Hogwarts to go on a solo adventure to find more about his family's past. He might travel to different wizarding communities that his parents were associated with, uncovering secrets along the way.
The story often takes on a more adventurous and dangerous tone. Without the relative safety of Hogwarts, Harry is exposed to the wider wizarding world in a different way. He might have to fend for himself more, rely on new allies, and face different kinds of magic and threats. For instance, he could be traveling to different wizarding communities that have their own rules and cultures.
Well, it might show Harry on a journey of self - reliance. He could be traveling alone, facing new challenges outside of the school's protective bubble. Maybe he meets new allies who help him understand the bigger picture of the magical world that Hogwarts had shielded him from.
One possible reason could be that she's frustrated with the school's bureaucracy. For example, if she constantly faces obstacles in getting approval for new study groups or advanced classes. Another reason might be a personal quest. Maybe she discovers a hidden mystery outside of Hogwarts that she can't explore while being a student there.
One possible reason in fanfiction could be that Snape's constant bullying and unfair treatment finally pushed Harry over the edge. Harry might have felt that he couldn't take it anymore, especially if Snape made his life at Hogwarts unbearable in ways that the other teachers didn't notice or couldn't stop.
It could also be due to personal reasons related to his growth and self - discovery. The events of the Triwizard Tournament might make him realize that he needs to find his own path outside of Hogwarts for a while. He might feel that the school can't offer him the answers or the experiences he needs at that moment to become stronger and more independent.
Well, her friends would surely miss her a great deal. Harry and Ron would feel like they've lost an important part of their team. Academically, the Gryffindor house might see a decline in grades as Hermione was often the one helping others study. Also, the teachers might be disappointed as she was a brilliant student.
Maybe the fanfiction portrays some really dark and disturbing events that make Harry feel he can't stay at Hogwarts anymore. For example, if it involves his friends being seriously harmed in the fictional story in a way that he can't bear to be associated with the place where it all seems to be happening.
One possible plot could be that Harry leaves Hogwarts to hunt down the remaining Death Eaters on his own. He might feel that he can't put his friends in danger anymore and takes it upon himself to rid the wizarding world of the last remnants of Voldemort's followers.