It could also be due to external threats. There might have been some outside forces that pressured the Third Hokage into making choices that seemed like a betrayal to Naruto. If an enemy threatened the village and demanded something related to Naruto, the Third Hokage, in his attempt to protect the village as a whole, might have made decisions that hurt Naruto.
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.
The Third Hokage was a symbol of stability in the village. Naruto, who grew up without parents and was sometimes an outcast, would see the Third Hokage as a source of strength and guidance. Also, the Third Hokage's knowledge of various jutsus and ninja arts could be something that Naruto admires in fanfiction, as Naruto is always eager to learn new techniques.
Naruto would probably be extremely hurt. He has always looked up to the Third Hokage as a grandfather figure. So, initially, he would be in denial, thinking there must be some misunderstanding.
One reason could be that there are political forces against him. Maybe some of the elders in the village don't trust his unorthodox ways and fear he'll bring too much change. Another could be that there are other candidates who seem more suitable on the surface, perhaps someone with a more traditional shinobi background who doesn't have Naruto's wild streak.
One possible reason could be that Naruto has seen the toll the position takes on those who hold it. Maybe he witnessed the stress and loneliness that previous Hokages like his father had to endure. He might want a more carefree life, exploring the world and spending time with his friends and family without the heavy burden of leading the village.
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.
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 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.
In this fanfiction, Naruto could be given a special mission by an unknown entity to save the Third Hokage. This mission might push Naruto to his limits and force him to unlock hidden potential within himself. Along the way, he might face challenges that test his loyalty and friendship.
Perhaps Naruto feels that the Hokage has been too strict or unfair in dealing with certain situations. Like if the Hokage didn't support Naruto's way of trying to bring peace and unity, which Naruto firmly believes in. This could lead to a growing resentment and eventually hatred.