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 way to justify it could be through a series of betrayals. Maybe Naruto discovers that Konoha has been using him all along, and his family has some dark secrets that make him feel betrayed. For example, if he finds out that his father was involved in some unethical experiments that led to the suffering of many villagers, that could turn him against both Konoha and his family.
A potential plot twist could be that Naruto's hatred is actually a cover - up for his love. He might be pretending to hate Konoha and his family to protect them from a greater threat. Maybe there's an enemy who would target them if Naruto showed any affection, so he creates this false front of hatred.
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.
Another way is through his attitude towards the villagers. He would show no respect or kindness to them. Instead, he would be cold and hostile, perhaps even going as far as to physically intimidate those who cross his path in Konoha.
In the original Naruto story, Naruto loves his village and eventually comes to understand and accept his family. But in this fanfiction, the hatred is a complete contrast. It changes the whole dynamic of Naruto's character and his relationships.
One possible reason could be a misunderstanding within the family. Maybe there were secrets kept from him that made him feel betrayed. As for Konoha, perhaps he felt ostracized or not fully accepted by the village despite his efforts, which led to his 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.
Another reason could be that he witnesses corruption or unfairness within the village leadership. If he sees that the system is rigged against certain groups, including himself or his friends, he could grow to hate Konoha and decide to leave.
The story could develop with Naruto leaving Konoha to find his own path. He might seek out other ninja villages or hidden places to train and become stronger on his own terms, away from the place and the family ties that he resents.