One possible reason could be that Sakura realizes Sasuke is on a path she can't follow. Maybe he's too consumed by his revenge and she decides it's better for her own well - being to leave him be. In some fanfictions, she might also find someone else who values her more and she chooses to focus on that new relationship instead of chasing after Sasuke.
In certain fanfictions, Sakura may leave Sasuke alone because she feels that she has tried everything to reach him but has failed. For example, she has continuously offered her support and love, but Sasuke remains cold and distant. So, she decides that it's time to respect his aloofness and move on with her life. This could lead to her exploring new friendships, career opportunities, or other romantic interests within the fanfiction world.
Protectiveness. Sasuke has seen a lot of danger in his life. He knows Sakura is a valuable person, both as a friend and as someone he cares about. So his possessiveness could stem from his desire to keep her out of harm's way. He doesn't want any bad guys to get near her.
One possible reason could be Sasuke's continued obsession with his revenge - even after they got married, his focus on past grudges might have driven a wedge between them. Another could be differences in their life goals. Sakura might have wanted a more settled family life, while Sasuke was still drawn to his wandering ways in the name of protecting the village from afar.
It could also be a way for the writer to express their own dissatisfaction with the original relationship between Sakura and Sasuke. Maybe they felt that Sakura's character was not well - developed in the context of that relationship and decided to create a more 'dramatic' storyline through cheating.
In fanfiction, Sasuke might snap at Sakura due to miscommunication. Sakura could be expressing her concern for him in a way that he misinterprets. For instance, if she tells him not to go on a dangerous mission and he thinks she is trying to control him instead of just caring about his safety. Another factor could be the influence of external forces. Maybe there are other characters or events that put him in a bad mood, and Sakura just happens to be there at the wrong time, so he snaps at her.
Sakura might cry over Sasuke because of the distance between them. In many fanfictions, Sasuke goes off on his own journey, leaving Sakura behind. She misses him and the pain of separation makes her cry. Additionally, if Sasuke gets injured severely in a fight, Sakura, being a medic, might cry out of worry for his well - being and the possibility of losing him.
One possible reason could be that Sasuke is too focused on his revenge. His single - minded pursuit of power and vengeance against Itachi leaves little room for romantic feelings. He might see a relationship with Sakura as a distraction from his goals.
Some writers might want to explore different character traits. They may think that Sasuke has a more complex personality that could lead him to make such a mistake. Also, it could be a way to show Sakura's reaction in a difficult situation and how she might grow or change because of it. In addition, it might be an attempt to break the traditional 'happy ending' mold of their relationship in the original story.
One reason could be to create drama. The idea of a relationship being broken by cheating is full of emotional turmoil which can make for an interesting read. Another reason might be some writers' preference for the Sasuke - Karin dynamic. They might see potential in their relationship that wasn't explored in the original series.
One reason could be that Sasuke realizes his true feelings for Karin were always there. Maybe in the fanfiction, he had some sort of epiphany that his connection with Sakura was more of a convenience or misunderstanding, while his bond with Karin was deeper on an emotional level.
One reason could be that in some fanfiction, the characterizations of Sasuke and Sakura might be off. Maybe Sasuke is portrayed as overly cruel to Sakura in a way that doesn't seem true to his character in the original series. Another reason could be that the storylines in these fanfictions are too clichéd, like always having Sasuke constantly reject Sakura in the same uninteresting ways.