One possible reason could be feeling ostracized. In the Naruto world, being different is often not easily accepted. As a female Naruto, she might face even more scrutiny and prejudice. Maybe she's tired of the constant expectations and the way she's treated in Konoha, so she decides to run away to find a place where she can be herself.
Perhaps she has a different vision for her life than what Konoha offers. She might have dreams of exploring the wider world, learning new jutsus from different places, or simply living a life free from the strictures of the village. Konoha has its own way of doing things, and if her ideals don't align with that, running away could be her way of seeking a new path.
Another reason could be for the sake of protecting the village. Maybe he discovers some sort of threat that he believes he can only face by leaving Konoha. He doesn't want the village to be in danger because of him, so he runs away to draw the danger away from Konoha.
She could encounter other outcasts. There are likely other ninjas or people in the world who have left their villages for various reasons. By meeting them, she could form a new group, a sort of 'family' of misfits. They could travel together, sharing their skills and stories, and maybe even start a small community away from the traditional ninja villages.
One reason could be that he feels misunderstood by the villagers. Despite all he has done for Konoha, some still hold grudges or are afraid of his power. Another might be that he wants to explore the world on his own terms, away from the responsibilities and restrictions of Konoha. Maybe he also feels a sense of loneliness there, as he has lost many important people and the village constantly reminds him of those losses.
One possible reason could be that he feels misunderstood. In the village, he has always faced discrimination because of the Nine - Tails inside him. People often look at him with fear and suspicion. So, he might run away to find a place where he can be accepted for who he is.
One possible reason could be that he feels misunderstood. In the Naruto series, Naruto often faced isolation and judgment from the villagers. If this extended to his family in the fanfiction, he might run away to find a place where he is accepted. Maybe he discovers some dark secrets about his family that make him feel unsafe or betrayed.
One possible reason could be that he felt misunderstood. In the village, Naruto was often ostracized despite his good intentions. Maybe he got tired of trying to prove himself and just ran away. For example, when the villagers still saw him as the nine - tailed fox rather than Naruto, it might have pushed him to leave.
One possible reason could be fear. Minato is a very powerful shinobi, and Naruto might be scared of him for some reason. Maybe he has heard stories about Minato that made him afraid.
One possible reason could be the constant scrutiny and pressure he faces in Konoha. Everyone has high expectations of him as the Jinchuriki of the Nine - Tails. He might feel suffocated by all the attention and the responsibility thrust upon him. Another reason could be the lack of true understanding from some of the villagers. Despite his efforts to protect Konoha, there are still those who look at him with distrust because of the Nine - Tails inside him.
It might be that his family is overprotective. Naruto is a very independent character. If his family in the fanfiction is constantly trying to hold him back from taking risks or going on adventures, he may feel suffocated. Running away would be his way of breaking free and exploring the world on his own terms.
One possible reason could be the constant feeling of being an outcast in the village. Despite his efforts, many villagers still look at him with suspicion because of the Nine - Tails inside him. He might feel that running away would give him a chance to find a place where he is truly accepted.