Perhaps in the fanfiction, Kushina lied about Naruto's potential. She could have downplayed his abilities to keep him from being targeted too early. Like, if Naruto showed signs of having a powerful chakra reserve or a unique kekkei genkai, she might have lied to the village elders or other shinobi about it so that Naruto could grow up without too much interference or jealousy from others.
One possible scenario could be that Kushina's spirit somehow manifests and guides Naruto in a difficult battle. She might use her chakra to give him an extra boost or share some long - forgotten family jutsu with him. Another scenario could be that in a time - travel fanfic, Kushina actually gets to be there in person to save Naruto from a dangerous situation in his childhood that he originally faced alone, like the time he was ostracized in the village as a child.
Perhaps Naruto lies to Kushina about something major. Let's say he gets into trouble at school and instead of being honest, he tries to cover it up. When the truth comes out, Kushina could be so disappointed that she cries. Or if Naruto decides to leave the village without telling her first, knowing how much Kushina loves him and wants him to be safe at home. This sudden departure could break her heart and make her cry.
Well, one scenario could be that Kushina finds a fanfiction where Naruto has turned evil due to some dark force. Another might be that she discovers a story where Naruto is in a relationship that is completely out of character for him. Maybe she stumbles upon a fanfiction where Naruto has some really strange and overpowered abilities that don't fit the original Naruto universe.
One scenario could be that Naruto discovers some hidden secrets about Minato and Kushina that he interprets as them being selfish. For instance, he might find out that they had a choice to be with him but chose something else instead, which makes him angry and full of hatred towards them.
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 interesting scenario could be Kushina protecting baby Naruto from some hidden threats in the village. She might use her unique Uzumaki abilities to keep him safe.
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.
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.
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.