Maybe it's because he hasn't mastered all the necessary skills or jutsus. Or perhaps he's underestimating the difficulty of the exam.
Maybe he realizes the exam is too dangerous or he discovers some unfairness in it. In the original Naruto story, Naruto has faced many difficulties and moral dilemmas during the Chunin Exam. So in the fanfiction, similar situations might push him to quit.
Naruto might feel unprepared because he hasn't mastered certain jutsu or lacks strategic thinking skills for the exam.
One possible fanfic could be about Naruto and Temari teaming up during the Chunin Exam in unexpected ways. Maybe Naruto helps Temari when she's in a tough situation against an opponent she underestimated. They could form an alliance that surprises everyone.
One possible scenario in such a fanfic could be Naruto easily overpowering his opponents during the Chunin Exam. For example, in the written test, he might use some new, godlike power to read the minds of the examiners or sense the correct answers. During the combat rounds, he could defeat his foes with a single move, leaving everyone in awe. His newfound power might be related to some ancient ninja art he discovered or a special training he underwent secretly.
Maybe it's due to a less engaging plot or unappealing characters. Not every manga can hit the mark for everyone.
Perhaps he was tricked into quitting. There could be some villains in the fanfiction who managed to deceive Naruto into believing that quitting was the best option for him. They might have used his naivete against him. For example, they could have told him that by quitting he was protecting his friends, when in fact they just wanted him out of the competition.
They could have a battle where Naruto discovers a new way to counter Temari's wind - based attacks. For instance, he might use his shadow clones in a creative way to disrupt the flow of her attacks.
Well, in the fanfic, there might be new and unexpected opponents. Maybe some characters who were not that prominent in the original chunin exam could have a big role this time.
Maybe it's because you're going through a phase of change or self-discovery. Sometimes our perception of ourselves can shift unexpectedly.
He might face disappointment from his friends and mentors. His friends who were also participating in the exam might feel let down, and his mentors, like Kakashi, could be concerned about his decision and how it will affect his future as a ninja.