The fanfic changes the relationship by introducing a negative aspect. Normally, Naruto values family and friendship. But here, if he hates his sisters, it means his family unit is not as harmonious as in the original story. It also might affect how he interacts with other characters in the story. For instance, if his friends try to reconcile him with his sisters, it could create new storylines and tensions. And it could also change how the village views Naruto, as a person who has family issues.
It could be that in the fanfic, Team 7 starts to act in a way that goes against Naruto's moral code. For example, if they start using cruel or unethical methods to achieve their goals. Naruto, being the character he is, would not stand for such behavior and this could lead to his hatred. Additionally, if there is a personal loss that Naruto experiences which he blames on Team 7, that would also contribute to his negative feelings.
One possible reason could be that Naruto's dad was not around during his childhood. In the Naruto story, Naruto grew up alone and ostracized, and he might feel that his dad abandoned him, which could lead to hatred in a 'dark Naruto' scenario.
Perhaps in the fanfic, there is a prophecy that says Naruto's friends will be the cause of his downfall. So, Naruto, fearing for his future and the safety of the village, starts to distance himself from them and eventually hates them. Or maybe his friends accidentally cause the death of someone Naruto loves dearly, which makes him unable to forgive them.
He could hate them because he felt they were absent during his difficult childhood. Naruto faced a lot of loneliness and bullying, and if he thought his parents could have prevented it but didn't, that would breed hatred.
It completely flips the original story. In the original, Naruto loves Konoha and eventually comes to terms with his family legacy. But in this fanfic, the hatred changes his character motivation. Instead of striving to protect Konoha, he might be out to get revenge or simply distance himself from it.
One possible reason could be that he feels neglected. Maybe his family was always too busy with other things and didn't give him enough attention. This lack of attention during his formative years could have led to feelings of resentment.
The fanfic might introduce new relationships. Since Naruto hates his family, he might form closer bonds with other characters who become like a surrogate family to him. This could lead to new story arcs focused on these new relationships and how they develop in contrast to his broken family ties.