In some fanfictions, Naruto might leave because of a rift within the village. If there are political factions that oppose him or his methods, and he feels that he can no longer operate effectively within the village, he may choose to leave. This could also be due to a misunderstanding or false accusations against him that he can't seem to clear up while remaining in the village.
One reason could be a sense of disillusionment with the village's leadership. Maybe they discover some dark secrets about the elders and decide they can't be part of it anymore. Another reason might be to protect the village in their own way. They could think that by leaving, they draw danger away from their home. Also, they might be seeking a greater power or knowledge that can only be found outside the village.
One possible reason could be a sense of disillusionment. Maybe Naruto discovers some dark secrets within Konoha's leadership that make him question his loyalty. For example, if he finds out that some decisions were made that put the village at risk for the wrong reasons.
One reason could be the motherly love. Kushina always loved Naruto deep down. Leaving him means missing out on his growth and important moments in his life. Another reason might be realizing the hardships Naruto faced without her presence. She probably feels guilty for not being there to protect him from the loneliness and the many challenges he had to endure in the village.
One possible reason could be that Naruto has a dangerous mission that only he can undertake. The safety of the village or the greater good might demand his immediate departure, even though it's hard for him to leave Hinata in such a state.
It could also be due to a power struggle. Naruto is extremely powerful and independent. If Rias or other members of the peerage try to control or limit his power in some way, he would not tolerate it. His power is a part of who he is, and he's used to using it freely to protect others. So this could lead to his departure from the peerage.
One reason could be that Naruto discovers some dark secrets about the village that make him lose faith in it. Maybe something related to the 'dark sage' in the story reveals a side of the village's history or leadership that he can't accept. Another reason might be that he's framed for a crime he didn't commit, and instead of waiting for the village to believe in his innocence, he decides to leave. It could also be that he feels restricted by the village's rules and wants to explore a different way of being a ninja, which the dark sage figure represents in some way.
Perhaps in the fanfiction, Sakura had some unique ability that was not accepted or was feared in the village at such a young age. This led to her family deciding to leave the village so that she could grow up without being ostracized or in danger because of this ability.
In some fanfictions, she might leave to fulfill a prophecy or a special mission. There could be an ancient prophecy that only she could fulfill, and it required her to leave the village at that young age. She might have been guided by some mysterious force or a vision that she believed was leading her towards her destiny.
One possible reason could be a mission. In many Naruto - related stories, missions often take characters away from their families. Naruto might have received a highly important and dangerous mission that requires him to be away from Kushina for a long time.
One possible reason could be a conflict within the team. Maybe Naruto felt misunderstood by Sasuke or Sakura. Another reason might be a mission gone wrong where Naruto blames himself and decides he's a liability to the team. Or perhaps he gets an offer from another group that he believes can help him achieve his goals faster.