One possibility could be that Naruto leaves Konoha and stumbles upon a village where everyone talks in rhymes. He tries to communicate but ends up making a comical mess of things. For example, when he asks for food, he says it all wrong and the villagers think he's performing a new kind of comedy act.
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.
He might encounter a hermit who lives in a tree and has some really strange habits. The hermit could offer Naruto some 'wise' advice that is actually just really absurd, like telling him to walk on his hands to find his true path.
This type of fanfiction concept is really out of the ordinary. Naruto's character is built on his values of friendship, loyalty, and his dream of becoming Hokage. Killing Sasuke would mean betraying all of that. However, in a fanfiction, the author might be exploring the 'what - if' scenario. For example, what if Sasuke's actions against Konoha were so heinous that Naruto felt he had no choice? But still, it's a far - fetched and very different view from the original Naruto we know.
It could lead to political unrest in Konoha. There might be those who blame the village leadership for Naruto's departure. This could lead to power struggles as different factions try to take control and change the way the village is run. Some might demand more transparency and better treatment of their shinobi to prevent such a thing from happening again.
Konoha's power structure could be affected. Naruto is one of the strongest shinobi in the village. Without him, the village might be more vulnerable to attacks from other villages or threats. They would need to quickly find ways to fill the gap in their defenses.
Sasuke might be more understanding. Given his own experiences of leaving Konoha, he could respect Naruto's decision. However, he might also secretly plan to keep an eye on Naruto from afar to make sure he is safe.
It could create a sense of unease and fear. Naruto is a very powerful ninja, and if he turns dark and leaves, the villagers would be worried about him coming back as an enemy. It might also lead to a decrease in morale among the ninjas who once considered Naruto a friend or ally.
In this fanfiction, perhaps Naruto leaves Konoha because he's being framed for something he didn't do. As he flees, he encounters Temari. Temari, being a strong - willed character, might be intrigued by Naruto's situation. She decides to help him clear his name. During this process, they travel to different places, learn about each other's pasts and dreams, and their relationship evolves from distrust to mutual respect and then to a deeper connection.
Well, perhaps Naruto is neglected in Konoha because of his past or the way he behaves. He leaves and stumbles upon a hidden village that has different values. There, he is welcomed and trained further. As he grows stronger, Konoha realizes their mistake. Naruto has to decide whether to forgive Konoha and return or stay in his new - found home where he is respected.