It could also be due to power struggles within the family. Naruto's growing power might threaten the existing power balance in the family. Some family members, fearing a loss of their influence, decide to reject Naruto to try and keep their power. For instance, if Naruto has a unique ability that could potentially change the family's long - established ways of doing things.
In the fanfiction, it might be that Naruto had different ideals and goals from his family. His strong will to pursue his own path of becoming Hokage, for example, could clash with the family's expectations, causing him to reject them.
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 reason could be that he wants to seek independence. Naruto has always been a bit of an outcast in his family, and he might feel that moving out is a way to prove himself and grow on his own. He could also be tired of the family drama or conflicts that might exist within the family unit in the fanfic.
He could be influenced by a powerful and mysterious force. This force might be something magical or a very strong jutsu that causes him to lose his memory and wander away from his family. In some fanfics, new and made - up powers can often play a role in such situations. Without his memory, he doesn't recognize his family and just drifts away.
Naruto might initially be heartbroken. He's a character who values family and connection deeply, so rejection would hit him hard. He could go into a state of self - doubt, wondering what's wrong with him.
It could also be due to a lack of support. Naruto was constantly in trouble and trying to prove himself. If his family didn't show up in any way to support him and Konoha didn't do enough to encourage him in a positive way, but rather just punished him for his pranks, he might grow to hate them both.
One possible reason could be some kind of dark magic or jutsu that has affected his family's memories. Maybe an enemy cast a spell specifically to make his family forget about him to weaken him.
One possible plot could be that Naruto's family, perhaps his parents if they were alive in this fanfic, reject him because of his status as a jinchuuriki. They might see him as a danger or a disappointment, which breaks Naruto's spirit who has always longed for family love.
One possible reason could be that he feels neglected. Maybe his family was always too busy with other things and didn't give him enough attention. This lack of attention during his formative years could have led to feelings of resentment.
He could be running away because of false accusations within the family. Just like how he was wrongly judged by the village in the original story, if his family wrongly blames him for something he didn't do, like stealing a family heirloom or causing harm to a family member accidentally, he might choose to run away rather than face their unjust wrath.