One possible reason could be Naruto's independent nature. He has always strived to make his own path and not rely on his father's legacy too much. So in the fanfic, he might refuse Minato to show that he wants to be his own person, not just Minato's son.
In the fanfic, Naruto might refuse Minato because of the pain Minato's absence has caused him in his life. He grew up without a father, facing many hardships. So when Minato shows up, Naruto could be angry and reject him out of all that built - up pain and resentment.
Naruto's character development includes learning about sacrifice and the importance of bonds. In the fanfic, his refusal of Minato could be a sign that he has outgrown the need for a father figure in the traditional sense. He has formed deep bonds with others like Iruka, Kakashi, and his friends. These relationships have made him strong enough to face Minato and say no if he feels it's necessary for his own growth and the protection of those he cares about.
Well, Naruto has had the advantage of learning from many great shinobi over time. He also has a unique bond with his friends which could potentially give him more strength. Minato, on the other hand, had a shorter lifespan to develop his powers. Naruto has had more time to grow and surpass his father in strength.
One possible reason could be Naruto's pent - up anger towards Minato for leaving him as an orphan. He might feel that Minato sacrificed himself without fully considering the consequences for Naruto.
It could also be that the plot of the fanfiction has Naruto in a situation where talking might put him or his loved ones in danger. So, for their safety and his own, he chooses not to talk.
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 for Naruto's protection. Maybe Minato knew of some great danger that was coming for Naruto and he thought that banishing him would keep him out of harm's way. Another reason might be related to some prophecy or hidden power within Naruto that Minato feared could be misused if Naruto stayed in the village.
It could be that he has some personal traumas related to fighting. For example, he might have seen the negative consequences of fighting in the past, such as the loss of loved ones or destruction of places he cares about, so he refuses to engage in it. In addition, he may also be influenced by certain moral or ethical beliefs within the context of the fanfic's world, which lead him to oppose fighting.
It could be that Naruto is trying to prove himself. He wants to show that he can be as great a fighter as his father. Also, he might have received some training or knowledge transfer from someone who knew Minato well. This could have inspired him to adopt Minato's fighting style. He may also be in a situation where his normal fighting style isn't working, so he turns to Minato's as a last resort.
One possible reason could be fear. If Naruto was 'godlike' in this fanfiction, his power might be uncontrollable and Minato, as Hokage, might feel it's a threat to the village. He could think that Naruto's power could attract too many dangerous enemies or cause destruction accidentally.
One reason could be guilt. Since Minato wasn't there for Naruto when he was growing up in the original story, in the fanfiction, he might be overcompensating for that lost time. He feels like he has to make up for all those years he wasn't around to protect his son.