Another reason could be a sense of disappointment. If Naruto had extremely high expectations of his family in the fanfiction, and they failed to meet those expectations time and time again, it could lead to his hatred. For instance, if he expected his family to support his dreams but they were constantly discouraging him.
It could also be due to some external influence. Perhaps an enemy manipulated Naruto's mind in the fanfiction, making him see his family in a negative light. This enemy might have used some form of mind - control or false memories to turn Naruto against his family.