Perhaps in a fanfiction, Sasuke discovers a new and extremely dangerous power that he can't control and it starts to endanger Konoha. Naruto tries to stop him but in the heat of the battle, accidentally kills him. Overwhelmed with guilt and feeling that the village will never understand, Naruto leaves. But this is a very different take on their relationship and the Naruto world as a whole.
In a more convoluted fanfiction plot, there could be a conspiracy within Konoha. The elders or some secret organization within the village wants Sasuke dead for some reason. They manipulate Naruto into believing Sasuke is a traitor and a danger. Naruto, being the naive and trusting person he can be at times, falls for it and kills Sasuke. Realizing he's been used, he then leaves Konoha in disgust.
Maybe they leave because of a conflict within Konoha. There could be political unrest or a group within the village that they don't agree with. They might think that leaving is the only way to avoid getting involved in something they don't believe in or to protect the village from the inside out in their own way.
They may leave to investigate a mystery that has long been ignored or covered up by Konoha. This could be related to the origin of certain powerful jutsu or the real history of some important clans. Their departure from Konoha is a way to break free from the village - imposed limitations on knowledge and seek the truth on their own.
One reason could be to seek a new life away from the constraints of Konoha. Maybe they feel that they can't fully grow or explore their potential within the village. Another reason might be to protect Konoha in their own way. They could believe that leaving and dealing with threats from the outside would keep the village safer.
With the villagers of Konoha, Naruto was once seen as a hero. But his leaving could cause mixed feelings. Some might see it as a betrayal, while others might respect his choice. Fem Sasuke was always an enigma in Konoha. Her leaving might be seen as expected by some, but for those who hoped she would fully integrate into the village, it would be disappointing. And as they journey outside Konoha, they will meet new characters, and their relationships with them will be based on their new identities as outcasts from Konoha.
Another reason might be that Naruto is seeking a greater purpose. In the fanfiction, his 'godlike' state could make him realize that there are threats out there that he can't face while being tied to Konoha. He may leave to protect the world on a larger scale, believing that he can be more effective away from the village.
One reason could be to seek greater power. Maybe they feel that Konoha no longer offers the training or resources they need to reach their full potential. So they decide to leave and explore other places where they can become stronger.
One possible reason could be to seek a new life away from the politics and pressures of Konoha. Maybe they feel restricted by the village's rules and expectations. Another reason might be for a personal adventure. They could be in search of something that Konoha can't offer, like a new type of ninja training or a mysterious power source. Also, it could be related to protecting their family. If they sense some kind of threat to their family within Konoha, they might choose to leave to keep them safe.
They could go to the Land of Fire's outskirts, where there are less - known ninja clans. Naruto might hope to learn from them and Anko could be interested in the unique fighting styles these clans possess.
One reason could be a special mission. For example, there might be a threat that only Naruto can help with in Suna. Maybe there's a new type of enemy that has some connection to Suna's unique chakra sources and Naruto's abilities are needed to figure it out.
One possible reason could be to seek new powers. Maybe they feel that Konoha no longer offers the kind of training or opportunities they need to grow stronger. Another reason might be to escape from certain politics or social pressures within the village. For example, Naruto has always been an outcast in some ways, and Ino might be tired of the family business or the way things are done in Konoha.