One possible reason could be a misunderstanding. Maybe Naruto overheard something his family said that he misinterpreted as them not loving or believing in him. For example, if he heard them talking about his wild nature or his past mistakes in a way that he took the wrong way.
Another reason might be that Naruto feels he has disappointed his family in some way. He could have failed at a big mission or made a choice that he thinks his family doesn't approve of. He might be so ashamed that he decides to isolate himself to avoid their disappointment.
One possible reason could be the burden of his past. Naruto has faced a lot of hardships and the memories might be overwhelming him, making him want to be alone. For example, the loss of his master Jiraiya might have left a deep scar, and he might feel that isolating himself is the only way to deal with that pain.
Perhaps he's dealing with some sort of trauma. For example, after the many battles he's been through, like the fight against Voldemort, he may be suffering from post - traumatic stress disorder. To cope with this, he isolates himself from others as he doesn't want to burden them or he's just too caught up in his own dark thoughts.
However, it could also have negative impacts. He might start to feel lonely and bitter, which could lead to him making some bad decisions. He could be more easily influenced by the wrong people or ideas because he lacks the grounding that his family usually provides. Also, his relationships with his friends might become strained as he tries to keep them at a distance too, thinking that they'll side with his family.
It could be that Naruto discovers some secrets within his family that make him feel uncomfortable or out of place. For example, if there are hidden agendas or dark pasts that he doesn't want to be associated with, he might choose to move away to start anew.
Naruto could be afraid of being seen as weak. In the ninja world, weakness is often frowned upon. He has a reputation to uphold, especially in front of his family. He doesn't want them to think that he can't handle his problems, so he hides his pain. He also might be trying to be strong for his family. If they see him in pain, it could affect their morale. So, he pretends that everything is okay to keep their spirits high and to give them the impression that they can rely on him no matter what.
One possible reason could be a long - held misunderstanding. Maybe Naruto discovers some family secrets that he misinterprets as betrayal or neglect. For example, if he finds out that his family had made some sort of pact that he disagrees with, it could lead to his rejection.
One possible reason could be that he has some unresolved issues from his past, like the absence of his parents during his childhood which made him feel a sense of detachment. Maybe he is so focused on achieving his ninja goals that he unconsciously starts to ignore his family. Another reason might be some sort of miscommunication within the family. For example, if there are secrets that the family has been keeping from him, he might feel betrayed and thus choose to ignore them.
One reason could be the shock of the revelation. Harry has always thought his parents were James and Lily. Discovering Snape is his father would be a huge shock, and he might isolate himself to process this new information.
One possible reason could be a misunderstanding. Maybe there was some miscommunication in the past that led Naruto to believe his family didn't understand him. For example, if his family had different expectations for his future as a ninja compared to his own dreams.
His relationship with the village would also change. The villagers, who have come to rely on Naruto as a hero, would be confused and perhaps a bit scared. Some might feel betrayed that he has isolated himself. But there could also be those who understand his need for solitude and wait patiently for his return.