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 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 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.
In the original Naruto story, Naruto has a strong desire to be part of a family and be accepted. However, in this fanfiction where he doesn't like his family, it completely flips that aspect. His family is usually a source of support and love in the original, but here it becomes a source of negative feelings for him.
Maybe Naruto just sees Sakura as a friend. He might have a different idea of his ideal partner and Sakura doesn't fit that. His feelings for her could be purely platonic.
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.
One possible reason could be his past traumas. Naruto grew up alone and was often shunned by the villagers. Physical touch might remind him of the times when he was pushed away or bullied, so he has developed an aversion to it in fanfiction.
Well, in some fanfictions, it might be because the writer wants to create an alternative storyline. Maybe they think Naruto has a different type of relationship in mind, like a more platonic or brother - sister - like bond with Hinata instead of a romantic one.
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.
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.