Perhaps he discovers a secret that makes him feel unsafe or uncomfortable in his current environment. This secret could be related to his family, friends, or the world he lives in. Running away seems like the only option to him to get away from this newfound danger or unease.
Maybe he's tired of his restricted life. In the story, he might be feeling suffocated by all the rules and expectations placed on him, so he decides to run away to find freedom.
It could be because of a conflict with someone important in his life. For example, if he had a huge fight with his father, who might be overly controlling in the fanfic, that could drive him to run away. He wants to escape the tense situation and find a place where he can be himself without that pressure.
Perhaps she is being chased by some unknown enemies in Konoha who are after her for some reason. She might think that running away from Konoha is the only way to protect herself and those she cares about. It could also be that she has a new mission or purpose that she believes can only be achieved outside of Konoha, and she is willing to sacrifice her life in the village for it.
Another reason could be that Naruto is being targeted by a powerful enemy within Konoha. He doesn't want to put his friends and the village at risk, so he runs away to draw the enemy away from Konoha. This would show his selfless side, sacrificing his own safety for the greater good of the village.
Another reason could be that Harry in the fanfic has a newfound sense of self - worth. He realizes he doesn't deserve the horrible treatment from the Dursleys and decides to break free. He may have learned about his true heritage in a different way in the fanfic and decides to leave behind the Dursleys, who have always tried to suppress his wizarding identity.
It could also be due to a particularly bad encounter with someone in the village. For instance, if he was bullied severely by some older kids and he felt that there was no one to protect him. He might have thought that running away was his only option to avoid further harm.
Mal might run away in the fanfiction because she's constantly being judged for her past as a villain's daughter. Despite her efforts to fit in Auradon, there are still those who look at her with suspicion. She could also be running away from a future that she doesn't want. For example, if there are plans for her to take on a role she's not ready for or doesn't believe in, she may choose to escape.
One possible reason could be that she feels trapped in the strict rules and hierarchy of the academy. Maybe she discovers some dark secrets within the academy walls that make her fear for her safety or the safety of those she loves. Another reason might be a conflict with a powerful figure at the academy, like a teacher or an elder vampire.
One possible reason could be to escape from false accusations. In the 'Harry Potter' universe, Sirius was wrongly accused of betraying the Potters. So in the fanfiction, he might run away to avoid being captured and to find a way to prove his innocence.
One possible reason could be Naruto's internal conflict. In yaoi fanfiction, the relationship is often complex. Naruto might be running away because he's confused about his feelings for Sasuke. He may not be ready to face the intensity of the relationship that the yaoi concept implies.
Maybe he discovers some dark secrets about his family. For example, if his parents were involved in something he considered unethical in the fanfic's plot. It could be that they were part of a group with a hidden and evil agenda.
One possible reason could be the pressure he feels in Konoha. Naruto has always been an outcast in the village to some extent. People used to fear and shun him because of the Nine - Tails inside him. He might feel that running away would be a way to escape all that negative attention and find a place where he could be himself without the constant reminder of his 'otherness'.