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.
It could be due to political reasons. There might be some sort of alliance or treaty being formed between Konoha and Kumo. As a symbol of trust and cooperation, Naruto, being one of the most powerful ninja in Konoha, is sent to Kumo. This way, it shows Konoha's commitment to the relationship and also allows Naruto to represent Konoha in Kumo's affairs.
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.
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.
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.
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.
Another reason could be that he witnesses corruption or unfairness within the village leadership. If he sees that the system is rigged against certain groups, including himself or his friends, he could grow to hate Konoha and decide to leave.
Well, in Kumo, Naruto might face challenges related to power struggles. There could be certain groups or individuals in Kumo who see Naruto as a threat to their own influence. He's a powerful ninja from Konoha, and some in Kumo might not want him to gain too much power or popularity there. Another biggie is making new friends. It's not easy to break into an established social circle in a new village, and Naruto might find it hard to find people he can really trust and rely on.
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.
Perhaps he discovered some dark secrets about Konoha that made him lose faith in the village. For example, if he found out that the village leaders were involved in unethical or immoral activities that were against his values, it could make him hate Konoha. He might also feel betrayed if his so - called friends turned their backs on him for some reason.
One reason could be to seek a new life away from the political drama in Konoha. Naruto has always been in the spotlight and has faced many political challenges. Hinata, being by his side, might support his decision to leave for a quieter place. Maybe they want to raise their family in a more peaceful environment, away from the constant threat of enemies targeting Konoha.