One possible reason could be a misunderstanding. Perhaps Naruto misinterprets some of his family's actions or words. Maybe he thinks his family didn't care about him as much as he thought they should. In fanfiction, authors often play with the idea of miscommunication and how it can lead to strong negative emotions like hatred. Also, if there are other characters in the fanfiction who influence Naruto's view of his family, say by spreading false rumors or manipulating him, that could contribute to his hatred.