It can change the power dynamics. If Kakashi fails Naruto, Naruto may not reach his full potential as quickly or at all. This could mean that some of the battles in the Naruto universe are lost or are much more difficult. For example, against Pain or Madara, Naruto might not be strong enough without proper guidance from Kakashi.
One possible scenario could be Kakashi fails to train Naruto properly. Maybe he misses some crucial aspects of Naruto's development, like not focusing enough on his chakra control early on. Another could be that Kakashi fails in a mission where Naruto is involved, perhaps due to miscommunication or underestimating the enemy.
In the fanfiction, Kakashi might fail because of external pressures. For example, he could be given other important missions that take up a lot of his time and energy. So, he can't dedicate enough time to Sasuke and Sakura's development. Also, he could be facing political pressure within the village that restricts his teaching methods or the resources he can use for their training. This would lead to him not being able to meet their needs and ultimately failing them.
In this fanfiction scenario, Kakashi's failure might cause Sasuke to be more reckless. Sasuke, feeling let down, could go off on his own more often. Sakura, who might have relied on Kakashi to keep Sasuke in check, would then be left to try and deal with Sasuke on her own. This could put a lot of stress on their relationship. She might be more desperate to bring Sasuke back to the right path, but Sasuke could see her as being too pushy, all because of Kakashi's initial failure.
If Naruto fails the academy in fanfiction, he might face a lot of disappointment from the villagers. They already look down on him, and this could make it worse. He might also lose confidence in himself and his dream of becoming Hokage could seem even more out of reach.
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.
One possible reason could be that Naruto faced an extremely tough opponent in the exam. Maybe the opponent had some special jutsu or skills that Naruto couldn't counter at that time. Another reason might be that Naruto made a critical mistake during the exam, like being overconfident and underestimating his enemy.