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.
The original Naruto storyline focuses on family bonds and love within the Uzumaki family. However, in this fanfiction, the 'naruto hates kushina' aspect goes against that. It might introduce new conflicts that were not present in the original. For instance, instead of Naruto having the support of his mother's legacy, he now has to struggle against his hatred for her, which could lead to different power - up scenarios or character developments.
In a fanfiction like this, Fem Kyuubi's love for Naruto could be a deep, almost possessive kind of love. Since Naruto has always been different from others in how he treats the Kyuubi. As for hating Kushina, it could be that Fem Kyuubi blames Kushina for separating her from the world for so long. And this could lead to a lot of internal conflict within Naruto, who loves his mother but also has a bond with Fem Kyuubi.
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.
Well, in some fanfictions, the idea of Naruto hating Kushina might be a very dark and twisted take. Maybe the author wants to explore extreme emotional scenarios. As for Naruto loving in this context, it could be about different kinds of love - like platonic love for his friends or a romantic love for a character. Fanfiction often takes liberties with the original story's relationships.
A fanfiction crossover between Naruto, Kushina and Fairy Tail could be really interesting. It could involve the unique powers from Naruto and Kushina's world combined with the magic in Fairy Tail. For example, Kushina's chakra chains could interact with Fairy Tail's ice - make magic in some creative ways. Maybe Naruto's shadow clones could be used in a joint mission with Fairy Tail wizards.
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.
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.
The fanfiction could develop this hatred through the introduction of new characters. These characters might feed Naruto false information about Minato and Kushina, making him question their motives and ultimately hate them. For example, a character who has a grudge against the Uzumaki family could manipulate Naruto.
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.