The dynamic between the characters would be completely different. Without Naruto, Sasuke would lack his main rival within the team. Their growth as characters might be stunted as they wouldn't have that constant push from Naruto. Also, Sakura would be missing an important friend and source of motivation.
One possible reason could be a sense of being undervalued. Maybe he felt that his teammates didn't fully appreciate his efforts during the Wave mission. For example, if Sasuke got most of the credit, Naruto might feel pushed aside.
Perhaps Naruto quits Team 7 in the fanfiction because of a betrayal. He might find out that one of his teammates has been secretly working against him or has lied to him about something really important. This could shatter his trust in the team and make him want to leave. Or it could be due to an accumulation of small incidents. Like constantly being the one to get in trouble for the team's mistakes, or not having his opinions heard when it comes to team strategies. Over time, these little things can build up and make him feel that he's better off on his own.
The remaining members of Team 7 could struggle without him at first. They might have to re - evaluate their own skills and teamwork. Eventually, they could either try to convince Naruto to come back or move forward and become stronger on their own.
It could also be due to a major disagreement with Kakashi. Maybe Naruto has a different vision for how they should operate as a team or a particular mission that goes against his values, causing him to leave.
If Naruto quits Team 7 in the fanfiction, it could introduce a whole new set of storylines. There could be a search for Naruto by Team 7, which would involve them exploring new places and meeting new characters. The emotional impact on the other characters would also be significant. Sakura might feel guilty, thinking she could have done something to prevent Naruto from leaving. Sasuke might be more conflicted about his own goals, as Naruto was always a driving force in his life. And Kakashi would have to deal with the failure of keeping the team together, which could lead to his own character development in unexpected ways.
One reason could be a sense of not being understood. Maybe Naruto feels like his teammates, Sasuke and Sakura, don't truly get him. Sasuke is often preoccupied with his own revenge, and Sakura has her eyes mainly on Sasuke. Naruto might feel left out and that his goals are not aligned with the team's, so he decides 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.
The story might shift the focus from the traditional Team 7 dynamics to Naruto's individual journey. Instead of the group going on missions together, Naruto could be on his own adventures, facing different challenges that he wouldn't have encountered in Team 7.
Naruto faces a whole new set of challenges. Firstly, the ANBU has a strict code of conduct which he needs to adapt to. The missions are often solo or with very small teams, so he has to rely more on himself rather than his comrades like in Team 7. Also, the enemies he faces in ANBU are often more powerful and cunning. He has to keep his identity a secret, which is a big change from his more open - natured role in Team 7.