He could also get angry. After all, being misjudged like that is unfair. His anger could lead him to either lash out verbally at Sakura or he could leave the village in a fit of rage, feeling that he is not accepted even by his friends. This could then lead to a series of events where Naruto has to find his own way and Sakura realizes her mistake later on.
Well, it could be that in this fanfiction, Naruto has some sort of hidden agenda. He might call Sakura ugly as a form of reverse psychology. He could be thinking that by doing so, she'll prove him wrong and become more confident. Or perhaps there's some miscommunication or misunderstanding between them. For example, Naruto misheard someone talking about Sakura in a negative way regarding her looks and he wrongly believes it, so he says she's ugly.
One possible reason could be Naruto's out - of - control power. If in the fanfiction Naruto has some new and extremely powerful abilities that he can't fully manage, Sakura might see him as a monster out of fear. For example, if he accidentally causes destruction while trying to save the village.
It might also cause Naruto to lose control more easily. If he hears such a hurtful term from someone he cares about like Sakura, it could make him more vulnerable to the Nine - Tails' influence. In the long run, it could be a turning point in his character development, either making him more bitter or more determined to show everyone, including Sakura, that he's not what she says.
In some fanfictions, it could be a situation involving a curse or a dark magic that Sakura doesn't understand. She has exhausted all her medical and ninja knowledge but to no avail. Naruto, on the other hand, has had experiences with all sorts of strange and powerful forces, so she begs him for help in order to save someone or something she cares about.
Well, it could strain their relationship a great deal. Sakura might feel hurt and become more distant from Naruto. She could also try to prove herself to him, which might lead to some interesting character development for her.
Naruto could be a bit hesitant at first if the situation is really complex or dangerous. He might need to think about the implications and if he is truly capable of helping. But in the end, his loyalty to Sakura and their friendship would likely make him agree. He might say something like 'Sakura - chan, don't worry. I'll do whatever I can.'
Sakura could prove them wrong by showing her medical skills. In many Naruto scenarios, her ability to heal the injured is crucial. For example, she was able to keep many ninjas alive during battles. Also, she has been training hard in combat. She might challenge one of the members of Team 7 to a spar and show her newfound strength and skills.
Well, in addition to Kakashi and Sakura, there might be other characters making brief appearances. For instance, Naruto could pop in for a short visit while Kakashi is there. Or maybe Tsunade could be mentioned, as Sakura's mentor, in relation to her current situation that led to Kakashi's house call. But at its core, it's about Kakashi and Sakura and their interaction.