Communication is key. Naruto and his sister could sit down and have an honest conversation about what's bothering him. They could clear up any misunderstandings that led to his hatred.
The story could end with Naruto realizing his hatred was misdirected. After some big event or revelation, he discovers that his brother and sister actually care for him deeply. They all reconcile and become a closer - knit family.
One possible reason could be jealousy. Maybe the sister is more favored by the villagers or has some special abilities that Naruto feels overshadow his own. This could lead to a sense of envy and ultimately hatred.
One common plot could be that the sister has a different ideology. For instance, she might believe in a more radical approach to achieving peace in the ninja world compared to Naruto's more inclusive and forgiving way. This difference could lead to clashes and eventually Naruto's hatred. Another plot could be a power struggle. If the sister is extremely powerful and uses her power in a way Naruto doesn't approve of, like being cruel to weaker ninjas, it could make Naruto hate her.
It could also be that Naruto has been influenced by some external force in the fanfiction. For instance, an enemy might have planted false memories or ideas in his head, making him believe that his parents and sister are bad. This false perception could then fuel his hatred.
In the original Naruto story, Naruto is mostly alone and doesn't have a twin sister at all. So this fanfiction completely adds a new character dynamic that doesn't exist in the original.
One possible reason could be a misunderstanding. Maybe some false information was spread about Kushina that made Naruto believe she had wronged him in some way. And for his sister, perhaps there was some sort of jealousy or miscommunication. For example, if his sister got more attention from their father or something similar.
Perhaps they have wronged Naruto in some way in the fanfiction. They could have betrayed him, like telling his secrets to others or getting him into trouble on purpose. This would lead to Naruto developing hatred towards them.
It could be due to a misunderstanding. Perhaps there was an incident where his sister was involved, but Naruto misinterpreted her actions as something malicious against him. Like she might have accidentally broken something precious of his and he thought it was on purpose.