Maybe Naruto has seen a side of Sakura that he doesn't like. It could be that Sakura has made some decisions in the past that Naruto doesn't agree with, like her initial infatuation with Sasuke that made her overlook some of Sasuke's more dangerous or unlikable traits. This could have made Naruto lose respect for her to some extent, leading to his coldness.
One possible reason could be that Naruto has his own unrequited love for someone else and he is trying to distance himself from Sakura to avoid leading her on. For example, if he has deep feelings for Hinata, he might be cold towards Sakura to make his own feelings clear.
One reason could be that Naruto is focused on his own goals like becoming Hokage and he might see Sakura's feelings or her actions as distractions. He has a lot on his plate and may not have the time or energy to deal with her in a warm way.
She might be confused at first. Sakura is used to Naruto being friendly and now his coldness would be a big change. She may start to question what she did wrong.
One reason could be that Naruto has been through so much himself and he might think rookies are naive. He's seen the harshness of the ninja world and doesn't want to coddle them. For example, he had to grow up without his parents and faced many life - threatening situations early on.
Another reason might be that Naruto has been influenced by external forces. Maybe he has made some bad friends or been involved in some situations that made him think being cold to his family was the right thing. He could have been brainwashed into believing that his family was holding him back from achieving something greater.
Well, in some fanfics, Naruko's coldness towards Sakura could be a result of a past event. Perhaps Sakura made a mistake that affected Naruko or someone Naruko loves. Another aspect could be the power dynamic. If Naruko is more powerful or has a special ability that Sakura doesn't, and Sakura shows envy or something similar, Naruko might react with coldness.
One possible fanfic could be that Sakura has resentment towards Naruto because she feels he doesn't understand her true feelings for Sasuke. But then, during a dangerous mission, Naruto saves her life in a heroic way. This act makes Sakura realize how much Naruto truly cares for her. In a moment of emotional turmoil, she impulsively kisses him, which then leads to a series of events where they have to confront their feelings for each other and also deal with the implications within their team.
Sakura might initially be confused. She has known Naruto for a long time and his sudden coldness would be unexpected. She may try to reach out to him to find out what's wrong.
It could also be related to Sakura's strength. Sasuke is constantly striving to become stronger. If Sakura somehow shows a weakness or makes a mistake during a fight that he thinks could have been avoided, and it has negative consequences for their situation, he might get angry at her for not being more capable.
Well, Sasuke's cold attitude could be a reason. He is often distant and unresponsive to Sakura's feelings in the original story, and in fanfiction, this can be exaggerated, making Sakura angry. For instance, if he ignores her attempts at conversation or help.
Jiraiya was a serious shinobi with a certain code. Fanfiction might play around with that code too much for his liking. It could make light of things he held in high regard, like his loyalty to the Leaf Village or his training of Naruto. So that's a possible reason for his hatred.