Well, in some Narusaku fanfictions, Sakura might hurt Naruto emotionally by choosing Sasuke over him repeatedly. This can make Naruto feel rejected and unloved, causing him pain.
Sakura could also hurt Naruto by not believing in his abilities in the context of fanfiction. For example, if she doubts his power during a crucial mission, it can wound his pride and self - confidence, which are important to Naruto. He always tries to prove himself, and when Sakura, who he cares about, doesn't have faith in him, it's a real blow.
In some narusaku fanfiction, Naruto might avoid Sakura because the story could be exploring different relationship dynamics. Maybe the author wants to create a more complex plot where Naruto has his own reasons, like he's focused on his ninja goals and doesn't want any distractions from Sakura at that moment.
In some fanfictions, Sakura might accidentally hurt Naruto during a training session. Maybe she uses a new jutsu she's not fully mastered and it goes wrong, hitting Naruto instead of the target.
In some Sasunaru fanfictions, Sakura might hurt Naruto emotionally. For example, if she chooses Sasuke over Naruto in a very cruel way, it can break Naruto's heart. She could say mean things about his dreams or his past as an orphan, which would deeply wound him.
In some fanfictions, Sakura might hurt Naruto's heart by rejecting his love in a particularly cruel way. For example, she could publicly embarrass him when he confesses his feelings, which would be a huge blow to his self - esteem and his love for her.
Naruto could also react with anger. He's not one to just take things lying down. If Sakura hurts him, he might lash out verbally. He could say things like 'I've always been there for you, and this is how you treat me?' expressing his frustration and pain. And then he might storm off, leaving Sakura to realize the impact of her actions.
Yes, there probably is. In the Naruto fandom, there are various fanfiction themes, and the 'narusaku' (Naruto - Sakura relationship) with Naruto hating Sakura can be an exploration of an alternative take on their relationship. Some fans might write this to explore what - if scenarios or to express their own views on the characters' dynamics that deviate from the canon.
One common element could be a significant event that causes Naruto to change his feelings towards Sakura. For example, he might discover something she did in the past that he can't forgive. Another element might be the exploration of how Sakura reacts to Naruto's hatred, which could lead to her character growth or downfall.
It could be due to Sakura's feelings for Sasuke. If she's overly focused on Sasuke and Naruto gets in the way of her plans regarding Sasuke in some way, she might lash out and hurt Naruto without really meaning to cause serious harm.
In other fanfics, Naruto might try to understand Sakura's perspective. He's a very forgiving person, so he could give her the benefit of the doubt and try to figure out what made her act in a way that hurt him. He might think that she had her reasons and try to work through it with her.
Naruto often shows his care through his actions. He might use his healing techniques on Sakura if she's physically hurt. For instance, if she has a cut or a broken bone, Naruto could use his medical ninjutsu skills, which he has learned over time.