One reason could be envy. Maybe Naruto sees Hinata as having something he doesn't, like a more stable family situation, and he lashes out in jealousy. Another reason might be that he's just being a typical, rambunctious kid who doesn't realize the impact of his words or actions on Hinata.
Well, it's not super common but it does exist. In some fanfictions, the 'Naruto bullies Hinata' scenario is used as a starting point to show character growth. For example, Naruto might start off bullying Hinata out of immaturity or misunderstanding, and then as the story progresses, he realizes his mistake and tries to make amends. This can lead to a deeper connection between them in the end.
Naruto's character would be presented as empathetic. He would understand how Ino feels when being bullied because he has been through it himself. So, he would not only save her physically but also try to comfort her emotionally. His character would also be depicted as strategic. Instead of just charging in blindly, he might first assess the situation and then use the most appropriate ninja technique to deal with the bullies. This would show that Naruto has learned to use his head as well as his heart in difficult situations.
One common theme is rivalry. The bullying can be seen as an extreme form of their rivalry. Another theme could be redemption, where Sasuke realizes his wrongdoings and tries to make amends.
One popular fanfiction might be where Hinata's bullying of Naruto is a misunderstanding. Maybe she was trying to get his attention in a really wrong way because she actually had a crush on him. For example, she could be stealing his lunch as a way to start a conversation, but Naruto takes it as bullying.
Sasuke would be furious. He already has a strong sense of justice and loyalty to Naruto. He'd likely immediately start looking for Naruto, using his Sharingan to track any possible leads. He might even go against the village rules if he thought the village was involved in Naruto's kidnapping.
Sakura might be really surprised at first. She could offer to help Naruto with his girl disguise, teaching him things like how to do his hair or choose the right clothes. She might also find it a bit funny but would be supportive in the end, seeing it as part of a mission. Sasuke, on the other hand, might be a bit more aloof. He would probably just raise an eyebrow at Naruto's new look but wouldn't make a big fuss about it as long as it was for a good reason.
His friends would be shocked at first. Sasuke might feel a sense of responsibility to find Naruto and bring him back. Sakura would probably feel guilty, especially if she was somehow involved in the situation that led to Naruto being cheated on.
Sakura would be worried sick. She might immediately inform Kakashi sensei and the rest of the village. Then, she would probably want to be part of the rescue mission. Sakura has grown stronger over time and would use her medical ninjutsu and combat skills to help save Naruto. She would also be constantly worried about Naruto's well - being and would encourage the others to move faster.