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 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.
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.
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 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.
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.
Another reason could be related to a prophecy or a hidden mission. They might have learned about a prophecy that required them to leave Konoha in order to fulfill it. This could involve finding a powerful artifact or learning a special technique that could only be achieved by being away from the village. Their departure would then be a sacrifice for the greater good of not just Konoha, but the entire ninja world.
It would create a sense of panic. Naruto is a very important figure in Konoha. His strength has been crucial in protecting the village. Without him, the villagers would fear attacks from other villages or threats from the Akatsuki. For instance, if the Akatsuki knew Naruto had left Konoha, they would likely see it as an opportunity to capture him more easily.
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'.
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.
Another reason might be a lack of acceptance. Despite all his efforts, if Naruto still feels like an outcast in Konoha, he could decide to defect. He might think that he can find a place where he is truly understood and valued elsewhere.