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.
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.
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.
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.
Maybe his sister is always favored by their parents, making Naruto feel left out and thus develop hatred.
One possible reason could be a misunderstanding. Maybe his team made a decision without consulting him, which made him feel left out and thus led to hatred. For example, if they took on a mission without him, Naruto, who values being part of the team, might feel betrayed.
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.
One possible reason could be that Naruto feels abandoned. His father was not around during his childhood, and he had to face a lot of hardships alone. Growing up without a father figure, he might have developed resentment.
One possible reason could be a misunderstanding. Maybe some false information was spread about Kushina that made Naruto believe she was a bad person. For example, if there were rumors that she abandoned him for some untrue reason, it might lead to his hatred.
It could be that Yugao has a connection to an enemy or a group that Naruto dislikes. This connection could make Naruto view her with suspicion and ultimately hatred. In some fanfiction scenarios, she could be unknowingly involved with a plot against Naruto or his village.
It could also be related to personal relationships. Tsunade might have been hard on Naruto in a way that he felt was unjust. Perhaps she was overly critical of his unorthodox ninja techniques or his impulsive nature, and over time, this built up into hatred. Naruto, being someone who values respect and recognition, could have resented her for not seeing his potential in the way he wanted.