Perhaps Naruto discovers some hidden aspect of his own power that is related to Minato's fighting style. Maybe there is a genetic or chakra - related connection that makes it easier for him to fight like Minato. He could also be influenced by the memories or stories he's heard about Minato. These stories could have motivated him to emulate Minato's fighting techniques.
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 reason could be a genetic quirk or some sort of chakra - related phenomenon. Maybe there was a hidden seal or something that was activated, causing Naruto to inherit not just Minato's looks but also his mannerisms. Another possibility is some kind of reincarnation or spiritual connection.
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.
Naruto could incorporate Minato's sword - fighting skills if he has any in the fanfiction. Minato was known to be proficient with weapons. Also, Naruto might use Minato's strategy of quickly assessing the enemy's weaknesses and then striking precisely at those points. He could even use some of Minato's signature jutsu in a more efficient way, like the Rasengan, but with Minato's finesse.
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.
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 possible reason could be a misunderstanding. Maybe Naruto gets involved in some dangerous situation and they disagree on how to handle it. For example, if Naruto wants to take on a powerful enemy alone but Minato and Kushina think it's too risky.
One characteristic is their similar determination. Minato was determined to protect the village at all costs, and Naruto has the same unwavering resolve. This determination drives them to keep pushing their limits and achieving great things.
One of the main similarities is their self - sacrifice. Minato sacrificed himself to save the village and his son. Naruto has also shown that he is willing to put himself in harm's way for the greater good. He's always the first to jump into a dangerous situation if it means protecting those he loves. Another aspect is their leadership qualities. Minato was a great leader as Hokage, and Naruto has developed into a great leader as well, inspiring those around him.
One possible reason could be that Naruto discovers some long - hidden secrets about Minato that he feels betrayed by. For example, if he found out Minato had made a deal that affected Naruto's life negatively in some way, like with the Kyuubi. Maybe Naruto feels that Minato sacrificed him for the greater good of the village without really considering his future or feelings.
One reason could be that Minato has some unfinished business with Naruto. Maybe he wants to pass on some crucial ninja skills or knowledge that only he can teach. Another reason might be the strong father - son bond. Despite being separated for so long, Minato's love for Naruto is still very deep.