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.
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.
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.
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.
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.
At first, their relationship might be a bit rocky. They both have strong personalities and different ways of doing things. But as they face challenges together, they start to understand and respect each other more. Their bond grows stronger as they rely on each other for survival.
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.
Well, it could be that Sasuke decides to join Naruto in leaving. They've always had a complex relationship. Maybe Sasuke sees Naruto's reasons for leaving as valid and decides to support him, which strengthens their bond.
They could leave because of a prophecy. Some ancient prophecy might state that they need to leave Konoha to fulfill a greater destiny elsewhere. So they trust in this prophecy and leave their home.
Maybe they leave to find a better way to protect Konoha. They might think that by exploring the outside world, they can gain new knowledge and powers that will be useful for their village in the long run.