One possible reason could be that he discovers a dark secret about his family. Maybe he finds out that his parents were involved in something dangerous or unethical in the wizarding world, and he can't bear to be associated with it, so he runs away.
It could also be that he is being targeted by some dark forces because of his parents. He runs away to protect his parents from having to constantly protect him. He believes that by leaving, he can draw the danger away from them and figure out a way to deal with it on his own.
He could go to Hogwarts early. Since he has some connection to the school already through his parents, he might think that the school could be a safe haven. There are also his friends' families there, like the Weasleys, who might take him in.
Maybe Harry feels a sense of guilt. In the context of the war, he might think that he's failed in some way by getting into this unexpected situation. He could believe that his new condition might put others at risk or that he's no longer the hero everyone expects him to be. So, to protect others or to avoid the shame, he decides to run away.
In fanfic, one reason could be that he might feel constantly in danger at Hogwarts. With all the dark forces targeting him, he could think running away is the only way to keep his friends safe. For example, if Voldemort's followers keep infiltrating the school, Harry might feel responsible and decide to leave to draw the danger away from others.
Hermione might run away from the Order because she discovers some secrets within the Order that she doesn't agree with. It could be something related to their decision - making process or how they handle certain information. If she runs away, she may try to form her own group to fight against the Dark side. This new group could bring fresh perspectives and strategies that the Order might be lacking.
One possible plotline could be that Harry runs away because he's tired of the constant danger at Hogwarts. He might find a hidden magical place where he can practice magic in peace and discover new spells on his own.
Maybe they were forced into it by some dark magic or a powerful dark wizard. They could have been blackmailed into betraying Harry to save their own lives or the lives of others they cared about.
There's a fanfic titled 'Escape and Rediscovery'. Female Harry Potter runs away after feeling betrayed by some of her so - called friends at Hogwarts. She travels far and wide, learning different forms of magic from various sources. It has a really unique plot and great character development.
One possible reason could be to explore different parenting styles in the wizarding world. Spanking, although a controversial form of discipline, might be used by some writers to show how Harry's parents could have dealt with difficult situations. Another reason might be for shock value or to create a unique and unexpected story within the familiar Harry Potter setting. It could also be a way for the writer to delve deeper into the characters' personalities and how they might react in a situation that involves discipline.
One reason could be fear. Snape has always been rather intimidating to Harry. Snape's cold demeanor and his past interactions with Harry's father might make Harry feel constantly on edge around him. So, running away could be an instinctual response to this fear.
One possible reason could be that in the fanfic, the author might twist the story to make it seem like his parents' actions had unforeseen consequences that affected Harry negatively. For example, their fight against Voldemort led to Harry being an orphan and having to bear a great burden from a young age.