Perhaps there were secrets in the family that Naruto discovered. In fanfiction, it's common to introduce hidden family secrets. If Naruto found out something like his family having a connection to an old enemy or some dark past, he could be angry and snap at them.
One possible reason could be a misinterpretation of family dynamics. Maybe in the fanfiction, the author portrays Naruto's family in a way that he sees as unfair or unloving. For example, if they are shown as neglecting him or putting too much pressure on him.
In the fanfiction, it might be that Naruto had different ideals and goals from his family. His strong will to pursue his own path of becoming Hokage, for example, could clash with the family's expectations, causing him to reject them.
Perhaps Naruto has some unresolved issues from his past that he doesn't want to burden his family with. He may think that leaving is the best way to deal with these issues on his own, without putting his family in the middle of his personal turmoil. He might go off on a solo adventure to find himself and come to terms with his inner demons.
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.
One possible reason could be miscommunication. Maybe Naruto misunderstands something Team 7 members say or do. For example, if they seem to be excluding him from a plan without a good explanation. Another reason might be stress. Naruto has a lot on his plate, and if Team 7 accidentally adds to his burden in the fanfiction, he could snap. Also, personal growth differences. If Naruto is growing in a different direction than the rest of Team 7 and they don't understand or support him, it could lead to him snapping at them.
Perhaps Boruto disrespects the ninja way that Naruto holds so dear. In fanfiction, Boruto could be shown as being too rebellious, and Naruto, as a firm believer in the ninja values, would snap at him to correct his behavior. For example, if Boruto were to shirk his training or mock the importance of teamwork, which are fundamental to Naruto's view of being a ninja.
In fanfiction, Naruto could snap at Minato due to the pressure he feels. Naruto has his own ideals and goals for the village, and if he feels that Minato's legacy or the way Minato is revered in the village is somehow hindering his own path or the changes he wants to make, he might lash out. He may think that Minato's actions, while heroic in the past, are now holding the village back in a modern context.
Perhaps continuous disappointment. If all his efforts to bring peace and unity were constantly thwarted, like his attempts at forging alliances between different ninja clans being undermined time and again. This build - up of frustration might lead him to snap and decide to leave in search of a new way or place where his ideals could be realized.
One possible reason could be a long - held misunderstanding. Maybe Naruto discovers some family secrets that he misinterprets as betrayal or neglect. For example, if he finds out that his family had made some sort of pact that he disagrees with, it could lead to his rejection.
One possible reason could be that he has some unresolved issues from his past, like the absence of his parents during his childhood which made him feel a sense of detachment. Maybe he is so focused on achieving his ninja goals that he unconsciously starts to ignore his family. Another reason might be some sort of miscommunication within the family. For example, if there are secrets that the family has been keeping from him, he might feel betrayed and thus choose to ignore them.