Naruto might be hurt by fanfiction in various ways. For example, some fanfictions could distort his character. They might portray him as overly cruel or weak, which goes against his original essence in the official story. This can mislead fans who are new to the Naruto universe and create a wrong perception of him.
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 some fanfictions, Team 7 might hurt Naruto through their words. For example, Sasuke could say something really mean about Naruto's lack of skills compared to his own in the beginning. Sakura might also be dismissive of Naruto's feelings for her in a hurtful way, which could make Naruto feel isolated within the team.
One possible fanfiction could be about Kakashi getting injured during a mission. Maybe he's protecting his team and takes a powerful jutsu head - on. His students then have to figure out how to get him to safety and find a way to heal him. It could show their growth as they face this difficult situation.
One reason is that some fanfiction authors may lack a deep understanding of Naruto's character. They might write things that are completely contrary to his values and personality just for the sake of creating a 'unique' story. For example, Naruto is known for his positive attitude and strong will, but in some fanfictions, he could be depicted as a negative or spineless character.
One possible reason could be a misunderstanding. Maybe Naruto was misidentified as a threat in a tense situation. For example, if there was some sort of dark jutsu at play that clouded Kurenai's judgment and made Naruto seem like an enemy. Another reason might be that Kurenai was under some sort of mind - control. There are many villains in the Naruto universe who are capable of such things. If she was being controlled, she might unknowingly attack Naruto.
One common theme is the test of friendship. When Kiba is hurt, his friends, like Naruto, Shino, and Hinata, come to his aid. This shows the strong bond among the Konoha shinobi.
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.
One common theme is misunderstanding. Often, Naruto may misunderstand Sakura's intentions or vice versa, which leads to one of them getting hurt. For example, Naruto might misinterpret Sakura's concern for him as pity, and his reaction could hurt her.