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.
Another reason might be related to Naruto's power. His growing power could be seen as a threat by some in the fanfiction. Kushina, in an attempt to protect Naruto from those who feared his power and might try to harm him, banished him. This way, he could grow and learn to control his power without the constant scrutiny and danger from within his original community.
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.
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 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 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 reason could be that she lost so much time with Naruto due to her early death in the original story. So in the fanfiction, she's overcompensating for that lost time by being possessive.
One possible reason could be that Kushina has a very strong and intimidating personality. In the Naruto universe, she was known to be a tough kunoichi. Naruto, who might be used to more gentle or reserved people around him, could be scared of her boldness.
One reason could be to explore the darker side of family relationships. In the Naruto world, family is often portrayed in a positive light, and this could be a way to show what could go wrong. Another reason might be to create a unique and attention - grabbing plot.