Perhaps in the fanfiction, Sarutobi betrays Naruto due to power politics. There could be a group within the village that wants Naruto out of the way because of his growing power. Sarutobi, being pressured by this group, decides to side against Naruto. This would completely change the dynamics of the Naruto world as we know it. It would create a lot of drama and conflict, which is often what fanfiction writers are aiming for.
In such a fanfiction, one possible reason could be a misunderstanding. Maybe Sarutobi is misled by false information about Naruto. For example, if some villains manage to plant evidence that makes Naruto seem like a traitor. Another reason could be for the so - called 'greater good'. Sarutobi might think that sacrificing Naruto would save the village from a greater threat. However, this would be a very controversial decision as Naruto is the main character and is supposed to be a hero in the original story.
One reason in this fanfiction might be related to Naruto's connection to the Nine - Tails. Sarutobi might fear that Naruto's link to the powerful demon could one day lead to the destruction of the village. He may think that by betraying Naruto, he can sever this connection and protect Konoha. But this would be a very shortsighted view as Naruto has shown time and time again that he can control the Nine - Tails' power and use it for good.
One reason could be the way Hiruzen treated Naruto as a child. In the original, Naruto was kind of an outcast, and if in fanfiction, Naruto blames Hiruzen for not doing more to prevent that, he could hate him. Another reason might be related to Hiruzen's decisions regarding the Uchiha clan. If Naruto in fanfiction feels that Hiruzen's actions led to bad consequences for the village and his friends, he might develop hatred.
It could be that Naruto has a different view of leadership than Sarutobi. Naruto might see Sarutobi's leadership as being too passive or too focused on maintaining the status quo. He, with his more energetic and revolutionary ideas, may resent Sarutobi for not being more progressive in making the village a better place for everyone, including himself.
Another reason might be related to a difference in ideology. Kakashi might have a different view on how to achieve peace or protect the village compared to Naruto. This divergence could lead to actions that Naruto interprets as betrayal. For example, Kakashi might believe in a more conservative approach that involves sacrificing some of Naruto's ideals in order to maintain the stability of the village.
One possible reason could be jealousy. Maybe Sasuke in the fanfiction becomes jealous of Naruto's growing power and decides to betray him for his own gain. Another reason might be a misunderstanding. For example, if Naruto is wrongly accused of something terrible, and the rest of Team 7 believes it without giving him a chance to explain, they could turn on him. It could also be due to outside influence. Perhaps an enemy manipulates Team 7 into believing that Naruto is a threat to them, leading to their betrayal.
One possible reason could be fear. Naruto is extremely powerful, and some in Konoha might fear that he could one day lose control of his power. Another reason could be political intrigue. There may be certain factions within Konoha that see Naruto as a threat to their power and influence. Also, jealousy might play a part. Naruto has achieved so much and has the love of many, and some might be jealous and thus plot against him.
Naruto would probably be extremely hurt. He has always looked up to Sarutobi as a leader and a father figure. His first reaction might be disbelief, unable to accept that Sarutobi would do such a thing. Then he would likely feel a great sense of anger and betrayal. He might lash out and try to prove his innocence.
Perhaps it was related to Naruto's heritage. The Third Hokage might have been influenced by some hidden secrets about Naruto's parents. If there were things he didn't want to come to light, he could have betrayed Naruto to keep those secrets buried. For example, if Naruto's father had enemies within the village, the Third Hokage might have tried to keep Naruto at a distance to avoid those old grudges resurfacing.
One possible reason could be a misunderstanding. Maybe Hinata is misinformed about Naruto's actions or intentions. For example, she might be led to believe that Naruto has done something harmful to the village when in fact he's innocent.
One possible reason could be past decisions made by Sarutobi that Naruto didn't agree with. For example, Sarutobi's handling of the Uchiha situation. Naruto, who values friendship and fairness deeply, might have seen this as a sign of Sarutobi's inability to do what's right, thus leading to his distrust.
One possible reason could be a misunderstanding. Maybe some false information was spread in the village that made Konoha believe Naruto had done something wrong. In fanfiction, things can be exaggerated and misinformation can easily lead to a situation of betrayal.