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.
From a security perspective, Konoha would be weaker. Naruto is a very powerful ninja, and Hinata is no slouch either. Their skills and abilities would be missed. Enemies might see this as an opportunity to attack Konoha. Also, Naruto has been a symbol of hope for the village. His departure could lead to a decrease in morale among the villagers. They might start to feel less secure and more pessimistic about the future.
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 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.
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.
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.
In this fanfiction, Naruto might leave because of the political situation in Konoha. There could be factions that he doesn't agree with or that are causing unrest. Naruto, being someone who values peace and unity, might find it difficult to deal with the internal politics and decides to leave in order to find a more harmonious place or to figure out a solution away from the chaos.
One possible reason could be that he feels misunderstood by his family. Maybe they have different expectations of him and he can't bear the pressure, so he decides to run away to Kumo to start a new life.
In fanfictions, Naruto could run away from his family due to emotional abuse. If his family members constantly put him down, criticize his abilities, or make him feel unworthy, he'd likely want to escape. Also, if his family is involved in some political intrigue that he doesn't want to be dragged into. For instance, they might be making deals with other clans that Naruto disagrees with. Additionally, if there is a new family member introduced, like a step - sibling who is favored over him and he feels unloved, that could prompt him to run away.
One possible reason could be to protect Naruto from the hidden threats in Konoha. Maybe she discovers some dark secrets or plots within the village that she believes will endanger Naruto, so she decides to take him away.
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'.