One possible reason could be a different upbringing in the fanfiction's alternate universe. Maybe he was raised in isolation or by people who influenced him to suppress family feelings. For example, if he was raised by a group that emphasized self - reliance above all else, he might grow up thinking family bonds are a weakness.
Well, it changes the emotional core. In the original Naruto story, family is an important underlying theme. Removing Naruto's feelings for his family shifts the focus. For instance, his motivation for becoming strong might no longer be related to impressing his father or living up to his family's name.
One plotline could be Naruto's journey to find out the truth about his family. He doesn't care about them initially, but as he uncovers secrets, his feelings start to change. Maybe he discovers that they had a noble reason for their actions that he misinterpreted.
One possible reason could be that in the fanfiction, his family might have been portrayed as overly strict or controlling. Maybe they forced him into a certain path he didn't want to take, like a particular ninja training regime that Naruto found too rigid.
One possible reason could be a misdirection in his goals. If in the fanfiction he is overly focused on proving himself to the village, he might think that family is a distraction. So, he starts to distance himself from his family to concentrate more on getting recognition from the village.
One possible reason could be some kind of dark magic or curse that has been placed on him. Maybe an enemy wants to weaken him by taking away his emotions so he can't fight with his usual passion.
One possible reason could be a misunderstanding. Maybe there was some miscommunication in the past that led Naruto to believe his family didn't understand him. For example, if his family had different expectations for his future as a ninja compared to his own dreams.
It could be due to some kind of misinformation. He might have been led to believe that his family didn't care about him, so in turn, he stopped caring about them. For example, if false rumors were spread about his family's intentions, it could warp his perception.
One possible reason could be that the fanfiction portrays his family in a way that goes against his ideals. For example, if his family is depicted as being involved in immoral or unethical activities, Naruto, with his strong sense of justice, would have a hard time accepting them.
It could be due to miscommunication. In the fanfiction, perhaps there were misunderstandings within the family. For example, Naruto might have overheard something that made him think his family didn't have his best interests at heart, but in reality, it was all a big mix - up. So, he gradually lost trust in them.