Maybe in the fanfic, Sakura has committed some unforgivable betrayal. For example, she might have broken a very important promise to the protagonist or she has caused great harm to someone the protagonist cares about deeply.
It could be that Sakura has been involved in some sort of deception in the story. Perhaps she has been lying about her identity or her intentions all along, and when the truth comes out, the character in the fanfic feels that it's just too much to forgive. This kind of plot device is often used in fanfics to create drama and conflict.
It could be because of a dark power corrupting Sasuke. Maybe an ancient evil force takes over him and makes him see Sakura as an enemy. In some fanfics, this kind of external influence can completely change a character's actions. Also, it might be related to Sasuke's pursuit of power. If he believes Sakura is standing in the way of his ultimate power - seeking goal, he could be driven to kill her.
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.
Maybe to explore different character arcs. The writer might want to see how Sakura would develop as a character if she strayed from her loyalty to Sasuke. It could also be a way to introduce new characters or relationships into the Naruto fanfic world.
One possible reason could be Sasuke's focus on his revenge. His thirst for vengeance against Itachi might make him blind to Sakura's feelings and neglect her as he is constantly preoccupied with getting stronger to achieve his goal of revenge.
In some fanfics, Naruto may ignore Sakura because he has his own emotional traumas to deal with. He might find Sakura's presence a reminder of things he wants to forget or move past, so he chooses to keep his distance. For example, if he has faced a lot of rejection from her in the past, he could decide to just cut her out of his life.
Another possibility is jealousy. Maybe in the fanfic, Sakura shows more interest in another character, like Sasuke perhaps, and Naruto, who has his own feelings for Sakura, snaps out of envy. It's a common trope in fan - made stories to play with the characters' emotions like this.
Perhaps they leave because they feel restricted in the village. They want to explore the world and grow as ninjas outside the boundaries and rules of the village. They might also want to learn from different ninja cultures and techniques that are not available in their own village.
Sasuke might believe that he's a danger to Sakura. Given his associations with dangerous elements and his own dark powers, he may feel that getting close to Sakura would put her in harm's way. Therefore, he rejects her to protect her. This is a common theme in many fanfics where Sasuke is portrayed as having a strong sense of self - sacrifice when it comes to Sakura.
One reason could be jealousy. If in the fanfic there's another character who Sasuke is close to, Sakura might be rude out of envy. Another reason could be that she feels betrayed by Sasuke in some way, like if he made a decision without considering her feelings. Also, it could be part of her own character development, starting off rude to show her flaws and then changing later.
Maybe in the fanfic, Sasuke has some personality traits that become more difficult for Sakura to handle over time. For example, his brooding nature might start to feel like emotional unavailability rather than just his usual self. This could lead to her regret.