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.
Perhaps Naruto himself doesn't want the position at that point in the story. He may feel that he still has a lot to learn or that there are other things he needs to do first, like finding a way to better the lives of the outcasts in the village or bringing about true peace among all the ninja villages without having to be in a position of such political power.
Sasuke could be an alternative. He has strong ninja skills and a deep understanding of the ninja world. His experiences have made him grow into a very capable person, and his Sharingan gives him an edge in combat and strategic planning.
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.
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.
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.
One reason could be the overwhelming pressure. Being Hokage means shouldering the safety and well - being of the entire village. Naruto might have realized that he can't bear that kind of stress forever. Another factor could be personal sacrifice. He may have seen how being Hokage has cost others in their personal lives and he doesn't want to go through the same. Also, he might have new dreams or goals that are not compatible with the role of Hokage, like exploring the world outside the village more freely.
One possible reason could be the overwhelming stress. Being Hokage means handling a lot of political, social and security issues in the village. Naruto might just feel that he can't take it anymore and decides to quit in the fanfiction. For example, dealing with the constant threats from other villages and internal disputes within Konoha can be mentally and physically exhausting.
One possible reason could be the pressure associated with the Hokage title. Naruto has always been in the spotlight and being Hokage comes with a huge burden of responsibility. Maybe in the fanfiction, he resents how it restricts his freedom to just be himself and have adventures like he used to.
In the fanfic, Naruto could hate the Hokage because of some bad experiences related to past Hokages. Perhaps he discovers some dark secrets about how the Hokage office has made decisions that he doesn't agree with. It might be something like a cover - up of certain events that Naruto believes should have been dealt with more fairly.
In some fanfiction scenarios, Naruto might jump off the Hokage monument to follow someone or something. For example, if there is a mysterious figure or a spiritual entity that he believes he needs to follow, and the only way seems to be by jumping. It could also be a symbolic act of breaking free from the expectations that come with being associated with the Hokage monument.
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.