There are multiple reasons. Firstly, the Third Hokage was highly respected in the village, and Naruto, being a part of the village, would naturally be influenced by this. Secondly, his wisdom in handling village politics and relations with other villages is something Naruto could look up to. In fanfiction, this could be explored more deeply, like Naruto learning from the Third Hokage's diplomatic skills to better protect the village in future interactions with other villages.
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.
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 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.
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.
Yes, in many fanfictions, Naruto is often depicted as a huge fan of the Fourth Hokage. After all, the Fourth Hokage is his father. Naruto grows up idolizing the Fourth Hokage's heroic deeds and wishes to be like him.
Yes. In some fanfictions, Naruto could be depicted as a big fan of the 4th Hokage. Since the 4th Hokage is his father, Naruto might idolize him for his great deeds and power. The 4th Hokage is highly respected in the Naruto world for sacrificing himself to save the village, and Naruto, growing up without knowing his true identity, could still be drawn to the legend of the 4th Hokage.
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.
It could be that in this fanfiction, Naruto has been influenced by some false information about the Fourth Hokage. Some villains might have spread lies about the Fourth Hokage's actions, and Naruto, being young and naive in the story, believes those lies and thus starts to hate the Fourth Hokage.
Naruto could be tired of the expectations placed on him. Everyone has always assumed he would be Hokage since he was a child. He might want to break free from those expectations and define his own path. He may feel that being Hokage is more about fulfilling others' wishes for him rather than his own true desires. So, he decides he doesn't want to be Hokage in this fanfiction.
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 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.