It could also be due to a falling - out with other campers or leaders. If there are misunderstandings or conflicts that they can't resolve, they might decide to leave. For instance, if they are wrongly accused of something and don't see a way to clear their names at the camp, running away could seem like the only option.
One reason could be to avoid a dangerous prophecy that they believe the camp can't protect them from. In some fanfictions, they might think that by running away, they can face the threat on their own terms.
In fanfictions, Naruto could run away from his family due to emotional abuse. If his family members constantly put him down, criticize his abilities, or make him feel unworthy, he'd likely want to escape. Also, if his family is involved in some political intrigue that he doesn't want to be dragged into. For instance, they might be making deals with other clans that Naruto disagrees with. Additionally, if there is a new family member introduced, like a step - sibling who is favored over him and he feels unloved, that could prompt him to run away.
One possible reason could be that he feels misunderstood. In the camp, everyone has high expectations of him as a son of Poseidon. If he makes a small mistake, it might be blown out of proportion. For example, if he accidentally causes a small flood during a training session, instead of being understood as still learning control over his powers, he could be harshly criticized. Another reason might be that he's tired of the constant danger at the camp. Every day there seems to be a new threat looming, whether it's a monster attack or some sort of internal camp conflict. He might just want to get away and have some peace for a while.
It could be due to a conflict with a particular authority figure at the camp. If he has a major disagreement with a camp leader over how to handle a situation, like dealing with a new enemy. Percy, being headstrong, might decide to run away and handle it his own way instead of following the camp's rules.
There are several possible reasons. Firstly, a sense of being controlled. If Edward is constantly making decisions for her or restricting her actions, Bella would want to break free. Secondly, self - preservation. If she realizes that the relationship is putting her in more danger than she can handle, she'll run. Thirdly, a change in her feelings. Maybe she falls out of love with Edward or realizes she was never truly in love, but rather in some sort of infatuation. So, she runs away to sort out her emotions and her life.
Perhaps in the fanfiction, Harry Potter runs away from Britain because he is disillusioned with the way the Ministry of Magic operates. There could have been a major event where the Ministry fails him or betrays his trust. Also, he may be seeking a place where he can explore his magic without the constraints and expectations that come with being 'The Boy Who Lived' in Britain.
Perhaps they run away because they are tired of all the rules and expectations placed on them. They just want to be free and explore the world on their own terms. They could end up in a small, idyllic town where they learn more about normal human life and each other away from the chaos of the demigod realm.
It could also be that in the fanfiction, Percy is given a new power or ability that Annabeth sees as a threat. Or perhaps Percy is made to side with someone Annabeth dislikes, causing her to 'hate' him in that fan - created story. This shows how different plot elements in fanfiction can change the dynamics between characters.
Perhaps the fanfiction is set in an alternate universe where something has happened to change Percy's feelings towards Annabeth. For example, if there was a betrayal in the fan - created story that made Percy turn against her.
Well, one possible reason could be that Percy made a really stupid decision without consulting Annabeth first. Like, if he went off on a dangerous mission on his own when they were supposed to be a team. Annabeth is a very strategic person and she might feel betrayed or extremely frustrated by such actions.
It could also be due to some sort of magic or mind - control. A powerful enemy might have cast a spell on Annabeth, forcing her to turn against Percy. In this case, it's not really her own will but the result of external manipulation.