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.
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.
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.
The first consequence could be a breakdown in the village's unity. Naruto is seen as a hero in Konoha, and if he turns against it, many of his supporters might be confused or even follow his lead. This could lead to internal strife within the village.
One possible reason could be that Konoha has a history of dark secrets. Maybe Naruto and Kushina discovered some unethical practices within the village that made them lose faith in it. For example, the way the village treated the Uchiha clan was quite unjust. Kushina might have known about some of these underhanded dealings and passed on her concerns to Naruto.
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.
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 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.
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.