Perhaps Naruto was falsely accused of something really serious in the fanfiction. Like he was thought to be involved with the enemy in some way. Kushina, being in a position of power, had to banish him to maintain the order and trust within the village, even if she didn't truly believe he was guilty.
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.
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.
In fanfiction, it could be due to a prophecy. Suppose there was a prophecy that Naruto would bring great danger to the village in the future. Tsunade, despite her bond with Naruto, might believe in the prophecy and banish him to prevent the foreseen disaster. Also, it could be related to Naruto's power. If his power was growing too rapidly and becoming uncontrollable, Tsunade might banish him to protect the village from any potential harm his power could cause.
One possible reason could be political pressure. Maybe some powerful clans in the village see Naruto as a threat due to his growing power and influence. They might force Tsunade's hand to banish him to maintain their own status quo in the village.
One possible reason could be fear. The villagers have always feared the Nine - Tails within Naruto. His family might banish him out of this same fear, not wanting to be associated with the potential danger he represents. Maybe they think that by banishing him, they can keep the village safe from the Nine - Tails' power getting out of control.
One possible reason could be some sort of dark influence or curse that makes her lose her maternal instincts. Maybe a powerful enemy targets her and in order to protect Naruto from further danger related to her, she feels forced to abandon him. Another reason might be that she is made to believe false information about Naruto, such as that he will bring great disaster to the village in the future.
One possible reason could be a mission. In many Naruto - related stories, missions often take characters away from their families. Naruto might have received a highly important and dangerous mission that requires him to be away from Kushina for a long time.
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.
Maybe she's been possessed. In some fanfictions, characters can be taken over by dark forces. So Kushina could be under the control of some evil entity and that's why she hurts Naruto.
One possible reason could be political. After the war, the villages might be restructuring and Naruto, with his great power, could be seen as a threat. Another reason might be related to the secrets he knows. Maybe some powerful figures don't want him to expose certain things. Also, his Jinchuuriki status could play a role. People might still be fearful of the power within him even after the war.