It could be a new character created by the author, like a young kunoichi from a small, far - away village. She might have special powers related to nature, like the ability to communicate with animals. This would make for an interesting dynamic when babysitting Naruto, as he's always been curious about different ninja abilities.
In this 'oc babysits naruto fanfiction', perhaps the OC is a ninja from another village who is visiting Konoha. They are assigned to babysit Naruto as a sort of cultural exchange or diplomatic gesture. Naruto, being his energetic self, wants to show the OC all his cool ninja moves, which the OC has to manage while also making sure Naruto doesn't get into real trouble. For example, Naruto might try to practice a new jutsu that could be dangerous if not supervised properly.
In the 'Akatsuki babysits Naruto' fanfiction, Pain might see Naruto as a potential tool or threat. He could try to indoctrinate Naruto into the Akatsuki's way of thinking. Meanwhile, Konan might be the more motherly figure, making sure Naruto is fed and clothed properly. Deidara might also be there, constantly arguing with Naruto about what is 'art' and getting into comical debates.
Itachi would be the most interesting babysitter. He has a calm and collected demeanor. He could handle Naruto's naughtiness with ease. His intelligence would also help him in understanding Naruto's motives and actions. He might also share some of his own experiences with Naruto, which could be both educational and inspiring for Naruto.
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.
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.
There are a lot of possibilities. Maybe Tenten would take Naruto on little adventures around the village while babysitting. They could visit the local ramen shop, and Naruto would of course be thrilled. Tenten could also tell Naruto stories about her own ninja training and adventures, which would inspire Naruto even more. Since Naruto doesn't have parents around, Tenten might also end up giving him some motherly - like advice and care.
Obviously, it's Tenten and Naruto. Tenten, with her skills and no - nonsense attitude, and Naruto, the energetic and sometimes mischievous ninja - in - training. Their interactions would be the focus of the fanfic, with Tenten trying to manage Naruto's behavior and Naruto likely trying to have as much fun as possible.