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.
He might be jealous because he secretly loves her. He doesn't want to see her with other people.
Well, it could be due to his dark past. Sasuke has been through a lot and sometimes in fanfics, that pent - up anger and trauma might make him lash out at Sakura. He might see her as an easy target because she's so close to him.
Well, it could be that in certain fanfics, the writers want to create a more complex and angsty story. Sasuke's character is often seen as a brooding and driven one. So, they make him hate Sakura perhaps because they think it adds an interesting dynamic. For example, if Sakura is constantly trying to get close to him but he hates her, it can lead to a lot of conflict and emotional turmoil in the story.
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.
Fanfiction sometimes goes against the essence of the original characters. Sakura, being a strong - willed character, might not want to be part of the Team 7 fanfiction where her character could be misused. For instance, she could be made into a weak or overly emotional character in fanfiction, which is not true to her original self. Also, the relationships within Team 7 in fanfiction might be warped in ways that she finds unacceptable, like false romances or rivalries that don't exist in the original story.
In the Naruto fandom, such a fanfic would be very out of character for both Naruto and Sasuke. They are comrades and friends with Sakura. However, some dark or AU (Alternate Universe) fanfics might explore extreme and unorthodox ideas. But in the main canon, they would never do this as they have a deep bond with Sakura. Naruto has been friends with her since childhood and Sasuke, despite his aloofness, also values her in his own way.
Another reaction could be that Sakura tries to follow Sasuke. She believes that she can change his mind or that she can be of help to him. She might leave her own responsibilities behind for a while to chase after him, thinking that their bond is strong enough to overcome whatever is making Sasuke leave.
Sakura would probably be initially very angry. She has strong feelings for Sasuke, but kidnapping is a very extreme act. So she would likely fight back, using her medical ninjutsu skills and combat abilities to try and escape.
In the fanfic, it could be that Sakura has her own reasons for not speaking to Sasuke. She might be trying to protect him in a strange way. She could think that by not speaking to him, she can keep him at a distance from some danger that she anticipates. It's a rather self - sacrificing act on her part.
They're popular because Sasuke and Sakura are well - loved characters from the Naruto series. Fans are always interested in exploring their relationship further. A lot of people ship them, so these fanfics give them the chance to see the two characters in different romantic scenarios.