One reason could be that he sees Naruto as a younger version of himself in some ways. Both have had their share of loneliness and challenges growing up. Kakashi may want to prevent Naruto from going through the same pain he did. Another reason is Naruto's importance to the village. As the jinchuriki of the Nine - Tails, Naruto is a key asset. Kakashi, being a loyal ninja, wants to protect the village's future which is tied to Naruto.
One great fanfiction is 'Kakashi's Unwavering Shield'. In this story, Kakashi goes to extreme lengths to protect Naruto from various threats within the village. He even stands up against the council when they try to make unfair decisions regarding Naruto. It really shows the depth of his protectiveness.
Well, Kakashi might constantly train Naruto privately to make him stronger. He would keep a close eye on Naruto during dangerous missions, ready to jump in and save him at any moment. For example, if Naruto is about to be attacked by a powerful enemy, Kakashi would use his Sharingan to quickly assess the situation and block the attack.
One key element is the bond. Kakashi sees a lot of himself in Naruto, especially the loneliness and the need to prove oneself. So he's extra protective. For example, in many fanfictions, he'll stop anyone from badmouthing Naruto because he knows how it feels to be an outcast.
Well, there could be. Fanfiction writers love to explore unique and unexpected relationships. Since Naruto and Kakashi are both popular characters in the Naruto universe, some writers might come up with such a plot for the sake of creativity and exploring different storylines. But it's not a part of the official Naruto story.
Sasuke could be a popular character. He might be involved in the story in a way that either helps or hinders the situation where Naruto hurts Kakashi. For example, if Sasuke tries to stop Naruto from doing something stupid that would hurt Kakashi.
Another reason could be related to Kakashi's past actions. If there are some secrets or things Kakashi did in the past that come to light and Naruto doesn't like them, he could snap at Kakashi. Naruto has a strong sense of justice and loyalty, so if he feels betrayed or misled by Kakashi, his reaction could be to snap.
One popular fanfiction is 'Kakashi's Unwavering Guard'. In this story, Kakashi becomes extremely protective of Sakura during a dangerous mission outside the village. He uses his skills and experience to keep her safe from various threats.
Kakashi might be initially surprised. But then, he would probably use it as a teaching moment for Naruto. He could say something like 'Naruto, stealing is not the way of a ninja.' And then give him a punishment like extra training.
One possible reason could be that Kakashi is preoccupied with other important matters in the village. Maybe he has some top - secret missions or tasks assigned by the Hokage that demand his full attention, leaving him with little time to focus on Naruto.