Well, it could be a misinterpretation on Sasuke's part. Maybe he thought Sakura was a threat to his goals at that moment in the fanfiction. He's always been very focused on his own path, and if he saw Sakura as getting in the way, he might lash out.
Sakura's ability to forgive and still care for Sasuke despite his past actions could also make him proud. In many fanfictions, she represents unconditional love. This selfless love and her ability to see the good in him, even when he was at his worst, could make Sasuke proud of her as a person.
In some fanfictions, Sakura's reaction could be more complex. She might be hurt not just physically but also emotionally. This could lead her to question her relationship with Sasuke and might cause her to make some big decisions, like whether to continue trying to reach out to him or to cut him off completely.
Maybe Sasuke sees Sakura's growth as a kunoichi. She has become strong and independent, and he admires that. So he wants her to be his.
Well, perhaps the writers feel that the Sasuke - Sakura relationship in the original was a bit forced. So they create fanfiction where Sakura doesn't love Sasuke to explore different relationship dynamics and character arcs for Sakura. For example, she could have a more platonic or even antagonistic relationship with Sasuke, which would be a fresh take on their characters.
In some fanfics, Sakura might avoid Sasuke because she's tired of his cold and distant attitude. She wants to surround herself with people who actually care about her and value her, so she chooses to stay away from Sasuke to find more positive relationships.
Well, Naruto has a very warm and persistent personality. He's always there for his friends, and he has a big heart. In fanfiction, Sakura might see these qualities in Naruto and realize his true value. He's the kind of person who can make her laugh and feel safe, which could be very appealing compared to Sasuke's more brooding nature.
Maybe for the shock value. It's not the typical view of their relationship, so it can attract readers who are tired of the same old storylines.
One possible reason in this fanfiction scenario could be that Sasuke feels a stronger connection to Karin on a spiritual or power - related level. Karin has unique abilities that might attract Sasuke more than Sakura's medical ninjutsu. Maybe he sees in Karin a kindred spirit in terms of their past traumas and the way they've had to fight to survive. Also, Karin has always been very devoted to Sasuke, and he might be drawn to that unwavering loyalty.
He may also choose to defend himself without really fighting back. Naruto values Sakura as a friend and teammate, so he would be reluctant to harm her. He might just try to dodge her attacks and keep talking to her, hoping to snap her out of it.
Sasuke could be sick of it because he values Naruto's strength and potential. He knows that Naruto is important for their village and for their future battles. Sakura hitting Naruto could potentially harm Naruto physically or mentally, which Sasuke doesn't want as it could affect their overall power balance and the future of the village.