Well, it can create a lot of tension. If Sasuke is used to Sakura being around or having certain feelings for him, her avoidance can make him question things. This can drive the plot as he might try to figure out why she's acting this way.
The avoidance can be a central conflict in the fanfic. The whole story could revolve around the reasons for Sakura's avoidance and Sasuke's attempts to resolve it. This conflict can bring out different aspects of both characters' personalities and lead to a series of events that build the overall plot, such as secrets being revealed or characters making unexpected decisions.
One possible reason could be that some fans might want to explore different character dynamics. In many fanfics, Sakura is often paired with Sasuke. But if the story focuses on Sakura avoiding Sasuke, it could be to break the typical mold. Maybe the writer wants to show Sakura's independence and growth outside of her relationship with Sasuke. For example, she could be on a journey of self - discovery and Sasuke represents a past she wants to move away from.
If Sasuke is a cold - hearted character at the start, seeing Sakura kiss someone might make him more empathetic. He might start to understand the complexity of human emotions better. For example, he could feel jealousy for the first time, which would be a new emotion for him to grapple with and could lead to his character evolving in terms of emotional depth.
Sasuke's jealousy can initially create turmoil. He may act out in ways that Sakura doesn't understand. This could cause friction between them. However, as they communicate more about his jealousy, it could lead to a deeper understanding. They might start to open up about their true feelings for each other. In the long run, this jealousy could be the catalyst that breaks down the barriers between them in the context of the arranged marriage.
It can create a lot of internal conflict. For example, Sasuke's depression might cause him to make rash decisions that drive the plot. He could isolate himself from Naruto and the rest of the group, which then leads to the others trying to reach out to him. This pursuit can form a major part of the fanfic's plot.
It can create a lot of tension. For example, it might lead to some intense confrontations between them. Their interactions would no longer be friendly or loving but full of anger and resentment.
He could also become more vengeful. If Sakura's death was caused by an enemy, Sasuke would stop at nothing to avenge her. His focus would shift solely to seeking revenge, and his already formidable skills would be honed even further in his quest for retribution.
It could make their relationship stronger in the long run. After the fight, they might realize how much they actually care about each other. They could start to communicate better and understand each other's perspectives more deeply.
In the original storyline, Naruto has a strong bond with Sakura, which includes his unrequited love for her at first. In the fanfic where he avoids her, it completely changes this dynamic. Instead of their usual interactions, there's a sense of distance.
The age difference can change the power dynamics. Since Sakura is older, she might be more confident and assertive in the relationship. For Sasuke, he could initially be a bit rebellious against her 'older and wiser' attitude, but over time, he might come to respect and rely on her more. It can add a whole new layer of complexity and growth to their relationship in the fanfic.
Often, it starts with Sakura having internal doubts and slowly realizing that things aren't as she hoped in her marriage. For example, she might notice that Sasuke doesn't communicate well with her.