One possible reason could be fear. If Naruto was 'godlike' in this fanfiction, his power might be uncontrollable and Minato, as Hokage, might feel it's a threat to the village. He could think that Naruto's power could attract too many dangerous enemies or cause destruction accidentally.
Maybe there was some sort of misunderstanding. Naruto's newfound 'godlike' abilities might have been misinterpreted. For example, some strange events might have occurred that made it seem like Naruto was using his powers for malicious purposes when in fact he wasn't. Minato, not fully understanding the situation, made the hasty decision to banish him.
One possible reason could be for Naruto's protection. Maybe Minato knew of some great danger that was coming for Naruto and he thought that banishing him would keep him out of harm's way. Another reason might be related to some prophecy or hidden power within Naruto that Minato feared could be misused if Naruto stayed in the village.
One possible reason could be for the protection of the village in a very extreme and controversial way. Minato might think that Naruto's presence is attracting too much danger and decides to banish him to keep the village safe.
One possible reason could be that Naruto discovers some long - hidden secrets about Minato that he feels betrayed by. For example, if he found out Minato had made a deal that affected Naruto's life negatively in some way, like with the Kyuubi. Maybe Naruto feels that Minato sacrificed him for the greater good of the village without really considering his future or feelings.
One possible reason could be for Naruto's protection. Maybe she thought by banishing him from a certain place or situation, she could keep him away from a hidden danger that she knew about. For example, there might be a powerful enemy targeting Naruto specifically, and she believed that by making him leave, he would be harder to find.
One possible reason could be a misunderstanding. Maybe some false information was spread about Kushina being a threat to the village, and Naruto, in his role as Hokage or a powerful figure, felt he had no choice but to banish her to protect the village. Another reason might be related to some sort of dark influence or curse that made Naruto act out of character and banish her.
It might be due to jealousy. If Minato was getting more attention or praise in the village for his achievements while Kushina felt overlooked, that could create resentment. Say, Minato was constantly being hailed as a hero for his speed and battle tactics, and Kushina, who also had great power, felt like she was in his shadow.
Naruto could also become determined. Since he is 'godlike' in this fanfiction, he might see this as an opportunity to grow even stronger away from the village. He might set out on a journey to master his powers fully and prove himself, with the intention of one day coming back to the village and showing everyone that he was wrongly banished.
It could be that Naruto is trying to prove himself. He wants to show that he can be as great a fighter as his father. Also, he might have received some training or knowledge transfer from someone who knew Minato well. This could have inspired him to adopt Minato's fighting style. He may also be in a situation where his normal fighting style isn't working, so he turns to Minato's as a last resort.
One reason could be guilt. Since Minato wasn't there for Naruto when he was growing up in the original story, in the fanfiction, he might be overcompensating for that lost time. He feels like he has to make up for all those years he wasn't around to protect his son.
Well, it could be that they find out some 'dark secret' about Naruto. Maybe they think he has some sort of uncontrollable power within him that they fear. Or perhaps they are forced to disown him due to political pressure in the village. There could be a group of elders or powerful clans that demand it in order to protect their own interests or maintain the so - called 'balance' in the village.