He could be on a quest for power. Iwa might have something unique to offer, like a powerful jutsu or a special training method that he thinks can make him stronger faster than in Konoha. And his family might not support this power - hungry side of him, so he decides to leave.
Maybe he feels ostracized in Konoha. If for some reason the villagers still don't fully accept him despite his heroics, he could be lured by the idea of a fresh start in Iwa.
Maybe Naruto has some sort of disagreement or falling - out with his family. This could lead him to seek a new start in Kiri. For example, if there are differences in values or expectations within his family that he can't reconcile with, he might choose to leave.
One reason could be that he feels betrayed in Konoha. Maybe some secrets were uncovered about the village's past actions towards him or his family that made him lose faith. So, he decides to start anew in Kiri where he hopes to find a different kind of acceptance.
In some fanfics, Naruto might leave his family because of a dangerous threat approaching them. He could believe that by leaving, he would draw the danger away and keep his family safe.
One possible reason could be that he discovers some long - hidden family secrets that make him feel betrayed. For example, if he finds out that his family was involved in something unethical in the past. Another reason might be that he feels constantly overshadowed by his family's legacy and can't form his own identity within the family, so he decides to leave to find himself.
One possible reason could be a threat from Iwa to Konoha. If Iwa was planning an unprovoked attack on Konoha, Naruto might take it upon himself to destroy Iwa to protect his village.
One possible reason could be a threat to Konoha. If Iwa planned an attack on Konoha, Naruto, as a defender of his village, might take the fight to them and end up destroying parts of Iwa in the process.
Another possibility is that they leave because of a sense of disillusionment. They could have witnessed some corruption or unfairness within Konoha's leadership or among the ninja community. This makes them lose faith in the village and decide to start anew elsewhere.
One reason could be to seek greater power. In fanfiction, the world outside Konoha might be seen as having more opportunities for growth. They might want to train with different masters or learn unique jutsu not available in Konoha.
One possible reason could be to protect her. Naruto might believe that by leaving, he can draw danger away from his sister. For example, if there are powerful enemies targeting him, he doesn't want his sister to get caught in the crossfire.
One possible reason could be to seek greater power and training opportunities elsewhere. Maybe he feels restricted within his clan in terms of the type of jutsu he can learn or the level of training he can receive. So, he decides to leave to explore different ninja arts and grow stronger on his own terms.