Another reason might be a prophecy or a special power within him that his family feared. Naruto has the Nine - Tails within him, but in this fanfiction scenario, it could be something else. His family, out of fear of this power, might have tried to suppress him. Feeling caged, Naruto ran away to explore and master this power without their interference.
It could be due to a family secret. Suppose his family was involved in something dangerous or unethical that Naruto couldn't bear. For example, if they had ties to an enemy organization that Naruto discovered. He is a character with a strong sense of justice, so running away would be a way to distance himself from their actions and figure out how to deal with the situation on his own.
One possible reason could be that he felt misunderstood. In the Naruto series, Naruto was often an outcast in the village. Maybe in this fanfiction, his family didn't understand his dreams or his need for recognition. So he ran away to find a place where he could be himself.
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.
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.
It could be that Naruto discovers some secrets within his family that make him feel uncomfortable or out of place. For example, if there are hidden agendas or dark pasts that he doesn't want to be associated with, he might choose to move away to start anew.
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 reason could be that Naruto feels constantly ostracized in the village despite his efforts to be accepted. In some fanfictions, he might run away because he discovers a dark secret about the village elders that makes him lose faith in the place he once called home.
He could be running away because of false accusations within the family. Just like how he was wrongly judged by the village in the original story, if his family wrongly blames him for something he didn't do, like stealing a family heirloom or causing harm to a family member accidentally, he might choose to run away rather than face their unjust wrath.
They would probably start searching for him. This could lead to the family members getting closer as they united in their goal to find Naruto. Or it could cause conflicts among them if they blamed each other for Naruto's running away.
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.
Some of his friends might feel betrayed. They could think that Naruto didn't trust them enough to share his problems about his family. For example, Sasuke, who has his own issues with family, might initially be angry at Naruto for running away instead of facing the family situation together like they face other challenges.