It could also be related to external forces. Maybe an enemy of the family or the village plants false evidence that makes Naruto seem like a danger. Since he is 'godlike', the family might believe the false accusations more easily, fearing his power, and expel him. Also, there could be a power struggle within the family, and those in power see Naruto's 'godlike' nature as a threat to their authority and use some excuse to kick him out.
Naruto might initially be shocked and hurt. After all, being expelled by his own family is a huge blow. But being 'godlike', he could quickly turn that pain into determination. He might decide to prove his worth and show his family that they made a big mistake.
It could be due to a perceived betrayal. Suppose Naruto discovers some dark secrets within his family that he can't overlook. In his 'godlike' state, he might be more morally rigid and thus decides to disown them. For instance, if he finds out that his family was involved in some unethical ninja practices in the past, he would feel compelled to distance himself.
It could also be due to some external influence. Perhaps an enemy manipulated Naruto's mind in the fanfiction, making him see his family in a negative light. This enemy might have used some form of mind - control or false memories to turn Naruto against his family.
One possible reason could be his unruly behavior. Naruto is known to be a bit of a troublemaker in the series, always pulling pranks. In fanfiction, this might be exaggerated, and the orphanage might not be able to handle it anymore. Another reason could be that he's suspected of being involved in something dangerous or illegal, even if he's innocent. For example, if there are strange incidents around the orphanage and Naruto is the easy target to blame because of his reputation.
One possible reason could be his prankster nature. Maybe he played one too many harmless but annoying pranks on the staff or other orphans, and they decided they'd had enough. Another reason might be the fear of the Nine - Tails within him. Even if the people in the orphanage didn't fully understand what it was, they could sense something dangerous about Naruto and wanted to distance themselves from him for safety reasons.
Iruka Sensei is often one of the characters. He has always been like a father figure to Naruto to some extent. In these fanfictions, he may offer Naruto a place to stay and continue to train him. Another one could be Jiraiya. He might take Naruto under his wing more so than in the original story, seeing Naruto's potential and his difficult situation.
Another plot could be Naruto's journey of self - discovery. After being kicked out, he realizes his own worth independent of his family name. He may focus on developing his skills even more, like his ninjutsu and his ability to make connections with people. He might start to understand that family doesn't have to be blood - related.
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.
In the context of this fanfiction, Naruto's family might banish him because they don't fully understand his 'godlike' powers. They see the surface level of his new strength and assume the worst. Maybe they think he has been corrupted by some unknown force. Also, it could be related to power politics within the family. Some members might see Naruto's power as a threat to their own position and influence, and so they convince the rest of the family to banish him to safeguard their own interests.
Another reason might be that Naruto has been influenced by external forces. Maybe he has made some bad friends or been involved in some situations that made him think being cold to his family was the right thing. He could have been brainwashed into believing that his family was holding him back from achieving something greater.