Maybe in this fanfiction, Sakura is involved in some kind of dangerous situation or plot that Naruto wants to avoid. He might leave to protect himself from getting too entangled. For example, if Sakura is part of a group that has different ideals which Naruto doesn't agree with and being around her means getting involved in those conflicts, he could choose to leave.
It could also be that Naruto has his own personal growth journey in the fanfiction. Sakura's presence somehow hinders his development or self - discovery. He realizes that he needs to be away from her to truly become the person he wants to be, perhaps to train in isolation or to explore new aspects of his ninja abilities without the distraction of his feelings for Sakura.
Well, it could be that Naruto feels he doesn't fit in Konoha anymore. Maybe he's constantly being misjudged by the villagers despite his efforts to protect them. Also, if his relationship with Sakura is a big factor in his leaving, it might be that he can't bear to see her with someone else, like Sasuke perhaps, and decides to leave to avoid the heartache.
One possible reason could be a mission. Maybe the Hidden Cloud Village (Kumo) requests Naruto's help specifically for a very important and dangerous mission that can only be accomplished by him. So, he has to leave Konoha for Kumo.
One reason could be that he feels ostracized. Despite his efforts to protect Konoha, some villagers still look at him with suspicion because of the Nine - Tails inside him. He might just get tired of constantly having to prove himself and decide to leave in search of a place where he can be accepted for who he is.
Perhaps they are forced to leave due to false accusations or being framed for something they didn't do. This could create a situation where they feel they have no choice but to leave Konoha in order to clear their names and also protect the village from the real threats that might be lurking in the shadows.
One reason could be that Naruto realizes his feelings for someone else and doesn't want to mislead Sakura. In some fanfictions, Naruto might discover that his true love is Hinata and so he steps away from Sakura to pursue a relationship with Hinata without causing any confusion for Sakura.
Perhaps he feels pressured in Konoha. Having a kid adds more responsibility, and he might think that leaving Konoha will give him the space he needs to grow as a father and a ninja without the constant eyes of the village on him. He could be seeking a place where he can train his kid in a different way, away from the traditional Konoha methods.
In the fanfiction, Naruto could leave Hozuki Castle because he feels out of place there. Despite his friendly nature, the culture or the people in the castle might be too different from what he's used to. He might long for the familiar environment of Konoha or his friends, and this homesickness drives him to leave, even if there were unfinished tasks at the castle. His departure could then lead to a journey of self - discovery as he tries to figure out where he truly belongs in the ninja world.
One possible reason could be his strong bond with Naruto. Their relationship has been through so much, and Sasuke might realize that Naruto understands him on a deeper level than Sakura. Maybe he feels that his journey and growth are more intertwined with Naruto's, and he values that connection more in this fanfiction.
Maybe Naruto realizes that his feelings for Sakura are not as strong as he once thought. In the fanfiction, he could have met someone else or had an epiphany about his own emotions. He might leave Sakura to find his true self and explore different relationships.
One possible reason could be her long - standing and deep - rooted love for Sasuke. Since childhood, she has had strong feelings for him. Maybe in this fanfiction, she realizes that her feelings for Sasuke are unshakable and that she can't continue to be with Naruto while having such intense feelings for another.