They could have run away because they were being wrongly accused of something at Hogwarts. In the wizarding world, rumors can spread quickly, and they might have felt that leaving was the only way to clear their names. Or maybe they found a lead on a powerful magical artifact that could be misused, and they decided to track it down without involving the school or the Order of the Phoenix.
Well, perhaps they ran away because they were tired of all the rules and restrictions at Hogwarts. Harry had always had a bit of a rebel streak, and Hermione might have finally agreed that they could achieve more on their own. Also, it could be related to a prophecy that they thought was best dealt with away from the prying eyes of their friends and teachers.
Well, perhaps they run away because they discover some dark secrets about the wizarding world that others don't want them to know. They might fear for their lives if they stay, so they choose to flee. It could also be that they are simply seeking adventure. The daughter of Harry and Sirius might inherit their adventurous spirits, and they both decide to run away to explore the unknown parts of the wizarding world and beyond.
One reason could be his ambition clashing with his family values. Percy is often very career - driven in the original story. Maybe in the fanfiction, his pursuit of success at the Ministry of Magic leads him to make decisions that isolate him from his family, ultimately causing him to run away. For example, he might be given an important assignment that goes against the Weasley family's stance on certain magical politics.
One reason could be she feels extremely pressured by the high expectations at Hogwarts. Everyone expects her to be perfect in academics and problem - solving. Another might be that she discovers some dark secret within the school that she's afraid of, like a hidden plot by a group of dark wizards among the staff or students. Or she could be running away to protect her friends. If she believes that her presence at Hogwarts endangers Harry and Ron, she might choose to leave to keep them safe.
Another reason could be a rift in their friendship caused by outside factors. For instance, if the wizarding community starts to turn against Harry because of false rumors or misinformation, Hermione might find it too difficult to stand by him. She may fear for her own reputation or safety, and this could lead to her abandoning Harry.
One possible fanfiction could be that they run away because they discover a dark secret within Hogwarts that the teachers are trying to hide. They fear for their lives and decide to flee to find a way to expose the truth on their own. They might head to the Forbidden Forest first, using their combined magical skills to avoid the dangerous creatures there and plan their next move.
Perhaps in fanfiction, Harry runs away from the Dursleys because he discovers a new threat that the Dursleys won't protect him from. He realizes that he has to take matters into his own hands and leaving is the only option. Also, he could be running away because he has made some new friends in the wizarding world who offer him a better alternative to living with the Dursleys.
One reason could be the trauma he endured during the war. He witnessed so much death and destruction that he might feel the need to escape it all. Maybe he wants to get away from the constant reminders of his friends who didn't make it.
Another reason could be that there are some misunderstandings between them. For example, Hermione might misinterpret Harry's actions or words as being too reckless or irresponsible, and she decides to push him away to avoid being dragged into what she perceives as a bad situation. Also, it could be related to her own insecurities. She might feel that she is holding Harry back in some way or that their friendship is becoming too complicated, so she takes the step of pushing him away to simplify things.
One reason could be to escape the constant danger at Hogwarts. Maybe there's a new dark wizard threat that the school can't protect him from. So he runs away to find a safer place to hide and train on his own.
One possible reason could be that Gon is on a quest for self - discovery. In the Hunter x Hunter world, there are so many mysteries and he might feel the need to explore on his own, away from his friends and mentors. He could be running away to find out more about his father, Ging. Maybe he thinks that by distancing himself from the normal Hunter path, he can uncover secrets that others are hiding from him.