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 a rift in their relationship over Boruto's ninja path. If Boruto decides to take a very different and unorthodox approach to being a ninja that Naruto doesn't approve of, such as using forbidden jutsu without proper understanding, Naruto might disown him in the fanfiction.
The plot could develop with Naruto creating his own new 'family' of sorts. He might gather like - minded ninjas who understand his vision. For example, he could team up with ninjas from other villages who also strive for a new kind of ninja world order.
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.
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.
It could also be due to some external influence. Perhaps an enemy used some kind of mind - control or manipulation on Kushina. They made her think that Naruto was a threat, so she decided to disown him. In the Naruto universe, there are many powerful villains who could potentially do this kind of thing.
It could be about Naruto achieving god - like powers and then getting involved in situations where his actions seem to go against his family values. Maybe he makes decisions that put his family at risk or goes against their wishes due to his new - found power.
One possible reason could be a misinterpretation of family dynamics. Maybe in the fanfiction, the author portrays Naruto's family in a way that he sees as unfair or unloving. For example, if they are shown as neglecting him or putting too much pressure on him.
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.
Perhaps Naruto has some unresolved issues from his past that he doesn't want to burden his family with. He may think that leaving is the best way to deal with these issues on his own, without putting his family in the middle of his personal turmoil. He might go off on a solo adventure to find himself and come to terms with his inner demons.
Perhaps there were secrets in the family that Naruto discovered. In fanfiction, it's common to introduce hidden family secrets. If Naruto found out something like his family having a connection to an old enemy or some dark past, he could be angry and snap at them.