Perhaps in the fanfic's storyline, there are some external forces at play. Some villain might have manipulated Kushina's mind, making her hate Naruto. This would add an interesting twist to the story as Naruto would then have to find a way to break this false hatred and redeem their relationship.
Maybe in this fanfic, the author wants to create a unique and dark plot. Kushina might be made to hate Naruto due to some kind of misunderstanding. For example, she could be misled to believe that Naruto has some connection to a great evil that she is against.
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.
Maybe in this fanfic, there has been a misinformation spread about Naruto that makes Kushina believe he has done something unforgivable. For example, if false rumors say that Naruto is involved in something evil, Kushina might start to hate him without knowing the truth.
Maybe she was forced to for some dark reason. Perhaps there was a threat to Naruto's life if she stayed, and she thought leaving was the only way to protect him.
Maybe in this fanfiction, there was some sort of dark magic or mind - control involved. Kushina could have been unknowingly influenced to do something that deeply hurt Naruto. Like she was made to abandon Naruto at a crucial moment in his life, which then led to his hatred.
One possible reason could be a misinterpretation of Kushina's actions. Maybe some events were presented in a way that made Naruto think she was neglectful or had made bad decisions in the past.
One possible reason could be a misunderstanding. Maybe some false information was spread about Kushina that made Naruto believe she was a bad person. For example, if there were rumors that she abandoned him for some untrue reason, it might lead to his hatred.
In some really complex fanfic plots, there could be a prophecy or some sort of ancient power play involved. Suppose there is a prophecy that Naruto will bring great destruction in the future, and Kushina is made aware of it through some dark magic or secret organization. She might think that betraying Naruto now is the only way to save the village and the world, even though it goes against her motherly instincts. This would be a very convoluted and interesting take on the idea of her betrayal.
One possible reason could be that Dark Naruto might see Kushina as a symbol of the world that rejected him. Since she was an important part of Naruto's family and the village, and Dark Naruto represents Naruto's negative emotions, he could resent her for the life he didn't have. He may feel that if Kushina had been there for him more (in his twisted view), he wouldn't have turned into this dark version.
Perhaps in this fanfiction, there is some sort of misinformation. For example, someone has spread false rumors about Naruto being a threat to the village, and Minato and Kushina believe it without proper investigation. This could lead to their hatred.
One possible reason could be for Naruto's safety. Maybe she has to go on a dangerous mission and believes Konoha is the safest place for him. Another reason might be that she is forced by some powerful enemies who threaten Naruto's life if she doesn't leave him in Konoha.