One reason could be the desire for more content. The official Naruto story has limits, but fanfic can offer countless new stories. For example, she might want to see different versions of her relationships with other characters.
She might be obsessed because fanfic allows for more character exploration. In the official Naruto series, her character might not have been fully developed in every aspect. Fanfic can give her more backstory, different personality traits, and new relationships. Also, it could be that she enjoys the creativity of the fanfic writers, who come up with unique ideas that the original creators might not have thought of.
It might be a relatively common thing among certain groups of Naruto fans. Fanfic offers a creative outlet for fans to play with the existing Naruto characters and storylines. Kushina being obsessed with it could be due to the fact that fanfic can provide new perspectives on her character. There are fans who are passionate about fanfic and those who aren't. But within the community of fans who like to explore the Naruto world more deeply, this kind of obsession could be quite normal.
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.
One possible reason could be for his safety. Konoha is a well - protected village with many skilled ninja. She might believe that leaving him there would ensure he has the best chance at survival and growth as a ninja. Also, she may have some mission or obligation that forces her to leave him behind, perhaps something related to the greater good of the village or the ninja world in general.
In some fanfics, there could be a misunderstanding. Suppose Kushina did something that Naruto misinterpreted as harmful to him or his friends. This misinterpretation could lead to his hatred. For example, if Kushina was involved in a mission that Naruto thought put the village at risk, but in reality, she had no choice.
This kind of fanfic is inappropriate because it can be very disturbing for fans, especially younger fans who are attracted to the Naruto series for its action, adventure, and positive character interactions. It can also damage the reputation of the fan community as a whole by promoting such unethical content.
Maybe it's because she sees Naruto's strength and how he has overcome so many difficulties despite her absence. She realizes that if she had been there, she could have made his journey easier. Also, she might regret not being able to watch Naruto grow up, miss his first steps, first words, and all those precious moments that a mother should be a part of.
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 could add to the popularity of certain types of fanfiction. If Kushina is seen as being obsessed with it, more fans might be interested in exploring the fanfictions she might be interested in. For example, if there are fanfictions that focus on Kushina's relationship with Naruto in new ways, those might gain more attention.
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.
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.