She may leave due to a prophecy or a vision she has. For example, she might see a future where the village is in danger and leaving is the only way to find a solution. So she ventures out, meets wise hermits or other powerful shinobi who guide her in understanding the prophecy better.
A simple reason could be for adventure. Sakura might be tired of the daily routine in the village and yearn for new experiences outside. So she decides to leave to explore the world and test her skills against new opponents.
Maybe it's to protect the village. He could discover a threat that he can only face away from the Leaf Village, to keep the danger from directly reaching his home and loved ones. He leaves as a form of self - sacrifice.
Perhaps they leave because they feel restricted in the village. They want to explore the world and grow as ninjas outside the boundaries and rules of the village. They might also want to learn from different ninja cultures and techniques that are not available in their own village.
One reason could be to seek greater power. Maybe they feel that Konoha no longer offers the training or resources they need to reach their full potential. So they decide to leave and explore other places where they can become stronger.
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.
Perhaps in the fanfiction, Sakura had some unique ability that was not accepted or was feared in the village at such a young age. This led to her family deciding to leave the village so that she could grow up without being ostracized or in danger because of this ability.
In some fanfictions, she might leave to fulfill a prophecy or a special mission. There could be an ancient prophecy that only she could fulfill, and it required her to leave the village at that young age. She might have been guided by some mysterious force or a vision that she believed was leading her towards her destiny.
She might leave to find herself. In Konoha, she has always been defined by her relationships with Naruto and Sasuke. Leaving gives her the chance to figure out who she is on her own terms, away from the expectations of her friends and the village.
Perhaps there have been disputes between the fanfiction community and the official Naruto representatives. For example, if the fanfiction community has been misusing or over - exploiting the Naruto character in a way that goes against the spirit of the original work. This could lead to the decision of asking Naruto to be removed from fanfiction.
Perhaps continuous disappointment. If all his efforts to bring peace and unity were constantly thwarted, like his attempts at forging alliances between different ninja clans being undermined time and again. This build - up of frustration might lead him to snap and decide to leave in search of a new way or place where his ideals could be realized.
One possible reason could be to seek a new life away from the politics and pressures of Konoha. Maybe they feel restricted by the village's rules and expectations. Another reason might be for a personal adventure. They could be in search of something that Konoha can't offer, like a new type of ninja training or a mysterious power source. Also, it could be related to protecting their family. If they sense some kind of threat to their family within Konoha, they might choose to leave to keep them safe.