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.
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.
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 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.
One reason could be that Loki feels constantly overshadowed by Thor. In the Asgardian hierarchy, Thor is often seen as the golden child. Loki, being the more complex and misunderstood one, might run away to find a place where he can be his own person without living in Thor's shadow.
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.
She could be running away due to family pressure. Her family might be forcing her into an arranged marriage or pushing her to join a certain dark - leaning group within the Slytherin community.
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 he can't accept, like a deal with a dangerous enemy. So, to avoid being associated with it, he runs away.
Perhaps he is on a quest for self - discovery. Jon Snow has always had a complex identity, and in fanfiction, he may feel that he can't fully understand himself while remaining in Winterfell. He runs away to explore the world outside, meet new people, and learn more about his true nature, which he hopes will ultimately make him a better leader or person.
One possible reason could be that Naruto feels like an outcast. Despite being part of Team 7, he might think that Sasuke and Sakura are closer to each other. Naruto has always been alone before joining the team, and if he feels excluded again, it could lead to him running away. Also, he might be afraid of endangering his teammates. Naruto often attracts trouble because of the Nine - Tails inside him. He may think that by leaving, he can keep his friends safe from the enemies who are after him for the power of the Nine - Tails.
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.