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.
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'.
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.
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.
To change her character dynamics. In fanfiction, if she's not from Konoha, her relationships with characters like Naruto and Sasuke will be different. Maybe she has a different loyalty or a different set of goals that are not related to Konoha's well - being.
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.
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.
A possible plotline could be that Sakura is from a secret organization against Konoha. She is sent as a spy, but as she lives in Konoha, she starts to question her loyalty and falls in love with the village and its people.
One possible reason could be that Naruto feels misunderstood in Konoha. Maybe some villagers still hold grudges against him despite his efforts to protect the village. He might run out to find a place where he can truly be accepted for who he is.
One possible reason is she's had an argument with her friends and feels she needs to get away to cool off.