It could also be due to a misunderstanding. Perhaps there was a miscommunication between Naruto and Sakura. For instance, Sakura said or did something that Naruto misinterpreted as her not really loving him, so he decides to leave in order to spare them both the pain of a relationship that he thinks is one - sided.
Maybe Naruto realizes that his feelings for Sakura are not as strong as he once thought. In the fanfiction, he could have met someone else or had an epiphany about his own emotions. He might leave Sakura to find his true self and explore different relationships.
It could also be that Naruto is forced to leave Sakura due to some external threat or danger. For instance, if there is an enemy targeting Naruto and he fears that being around Sakura will put her in harm's way, he would choose to leave to keep her safe. This is in line with Naruto's selfless nature as seen throughout the series.
One possible reason could be to seek stronger opponents outside of Konoha. Naruto might feel that he has outgrown the training opportunities in the village and wants to face greater challenges.
One reason could be that Naruto realizes his feelings for someone else and doesn't want to mislead Sakura. In some fanfictions, Naruto might discover that his true love is Hinata and so he steps away from Sakura to pursue a relationship with Hinata without causing any confusion for Sakura.
One possible reason could be that Naruto has a different love interest in his heart, like Hinata. In the original story, his relationship with Sakura was more of a friendship - like bond. Another reason might be for the sake of creating an unexpected plot twist in the fanfiction. Maybe the writer wants to explore different emotional and relationship dynamics that don't follow the typical Naruto - Sakura pairing.
One reason could be that Naruto has always been more attracted to those who understand his outcast past better. Sakura doesn't really have that kind of connection with him as she comes from a more normal background. So there's a lack of that fundamental understanding between them which hinders any romantic feelings.
One reason could be jealousy. If in the fanfic, Sakura gets closer to someone else Naruto cares about, like Sasuke in a different way than he expected, it might make him hate her. For example, if Sakura teams up with Sasuke against Naruto's wishes in the fan - created plot.
In some fanfictions, it could be due to unrequited love. If Naruto has deep feelings for Sakura but she continuously rejects him in a cruel or thoughtless way, Naruto might feel angry enough to seek revenge. For example, she could publicly humiliate him for his feelings, which would hurt Naruto deeply and lead to thoughts of revenge. Another reason could be a misunderstanding. Suppose Sakura is misjudged by Naruto as having done something terrible when in fact she was innocent. But Naruto, in his ignorance, decides to take revenge. This can create a lot of drama and conflict in the fanfiction.
One possible reason could be jealousy. Maybe in the fanfiction, Naruto feels overshadowed by Sasuke in Sakura's eyes, which leads to his hatred. Another reason might be that he perceives their relationship as a threat to his own bonds with them. For example, he could think that Sasuke and Sakura's closeness excludes him in some way.
One possible reason could be that Naruto has his own goals and missions that he is so focused on that he tries to avoid distractions, and Sakura might be seen as a distraction in some sense. For example, he is always aiming to become Hokage and improve his ninja skills, and any personal relationship drama could get in the way of that.
One possible reason could be that she sacrifices herself to save Naruto from a powerful enemy. In the heat of battle, she might put herself in harm's way to ensure Naruto's survival.