Perhaps in this fanfiction, Harry discovers some dark secrets about his family. Maybe he finds out that his family had some sort of connection to dark magic in the past and he hates them for not being the noble family he thought they were. Also, if he has been compared unfavorably to his family members all his life, like to James Potter who was popular but Harry has always been an outcast at the Dursleys, that could breed hatred.
One possible reason could be the way the Dursleys treated him. They were cruel, made him live in a cupboard, and constantly belittled him. This kind of mistreatment over the years could easily lead to hatred. Another aspect could be the lack of connection to his wizarding family that he was not aware of for a long time. He might feel angry at his parents for leaving him in such a situation without any real protection from the Dursleys.
One possible reason could be that he might feel abandoned. Growing up without them, he could resent the fact that they left him an orphan. He might think that if they were really so great, they would have found a way to survive and be there for him.
One possible reason could be that his family in the fanfiction might be cruel or neglectful towards him. Maybe they constantly put him down or don't support his dreams and ambitions, which would lead to his hatred.
One possible reason could be that in the fanfic, the author might twist the story to make it seem like his parents' actions had unforeseen consequences that affected Harry negatively. For example, their fight against Voldemort led to Harry being an orphan and having to bear a great burden from a young age.
In some fanfictions, his family might be involved in dark magic or have a bad reputation. So, Harry Potter refuses them to uphold his own moral values. He is known for his strong sense of right and wrong, and if his family goes against that, he would distance himself.
It could also be due to a lack of support. Naruto was constantly in trouble and trying to prove himself. If his family didn't show up in any way to support him and Konoha didn't do enough to encourage him in a positive way, but rather just punished him for his pranks, he might grow to hate them both.
One possible reason could be that he discovers some long - hidden family secrets that make him feel betrayed. For example, if he finds out that his family was involved in something unethical in the past. Another reason might be that he feels constantly overshadowed by his family's legacy and can't form his own identity within the family, so he decides to leave to find himself.
In some fanfictions, Harry might leave his family because of a prophecy or a special mission. He might feel that he has to go it alone in order to fulfill this prophecy or complete the mission successfully. His family might not understand or be able to support him in this, so he decides to leave. Also, there could be jealousy or resentment within the family that makes the environment unbearable for Harry.
One possible reason could be the betrayal he faced from some people in the wizarding world. For example, some students at Hogwarts might have spread false rumors about him or treated him unfairly because of his fame as 'The Boy Who Lived'. This could have led him to develop a general dislike for humans.
It could also be due to differences in values. If Dark Naruto had different beliefs about power, friendship, or loyalty compared to his family, and they constantly clashed over these, it might lead to his hatred. For instance, if his family adhered strictly to Konoha's traditional values but he saw them as restrictive.
One possible reason could be feeling neglected. Maybe his family was always preoccupied with other matters, like protecting the village, and didn't give him enough attention. So he grew to resent them.