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.
Perhaps he's been influenced by an outside force. Maybe he's been tricked or manipulated by an enemy. This enemy could have made him believe that quitting the exam is the best option for him or his village. They might have planted false information in his mind, causing him to lose faith in the exam process and ultimately decide to quit.
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.
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.
He might face disappointment from his friends and mentors. They had high hopes for him in the exam, so his quitting could lead to some strained relationships at first.
Naruto would likely become more self - reliant. As a ronin, he doesn't have the support of a village. So during the Chunin Exam, he has to trust his own instincts and skills more. He may also become more cautious as he realizes he can't always count on backup.
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.
Maybe in a fanfic, Naruto is dealing with a personal crisis or a family matter that makes him unable to attend the Chunin Exam. Or perhaps there's a magical curse that keeps him away from it.
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.
One possible reason could be that Naruto faced an extremely tough opponent in the exam. Maybe the opponent had some special jutsu or skills that Naruto couldn't counter at that time. Another reason might be that Naruto made a critical mistake during the exam, like being overconfident and underestimating his enemy.
Maybe it's because he hasn't mastered all the necessary skills or jutsus. Or perhaps he's underestimating the difficulty of the exam.
One possible fanfiction could be about Sakura showing off her improved medical ninjutsu skills during the Chunin Exam. She might use her skills to quickly heal her teammates during battles, surprising everyone with her growth.