One possibility could be that Naruto discovers a long - hidden secret about his family that makes him feel betrayed. For example, he might find out that Minato and Kushina had made a deal with a dangerous enemy in the past that put the village at risk. This would be so against Naruto's values of protecting the village and his friends that he decides to leave them.
If Kushina leaves Minato for Naruto in fanfiction, it would completely change the Naruto universe's family dynamics. Naruto might grow up with a different kind of support system. Instead of the absent father figure of Minato, he could have a more present mother figure in Kushina. This could also change his relationship with the village. Since Kushina was an Uzumaki, her presence could lead to Naruto having an earlier understanding of his heritage.
I'm not sure specifically as I haven't read that particular fanfiction. But generally, it might be about Kushina leaving Minato and could explore their relationship, the reasons behind such an action, and how it impacts the Naruto universe within the creative context of the fanfic.
He would likely become more self - reliant. Without Minato and Kushina's guidance, Naruto would have to figure things out on his own. He might make more mistakes at first, but those experiences would toughen him up.
On a more personal level, they could face internal guilt. As Naruto grows up and achieves great things on his own despite their neglect, Minato and Kushina may realize what they've missed out on. This realization could cause them a great deal of internal turmoil and regret for not being there for their son when he needed them.
In many Naruto fanfictions where Naruto meets Kushina and Minato, it often creates a very emotional scenario. Naruto finally gets to meet his parents who he has only heard about. It could be a heart - warming reunion where they share stories, hugs, and Minato and Kushina get to see how far Naruto has come.
Naruto's character would likely be more confident. With Kushina by his side, he'd have someone to constantly affirm him. He might not have the same desperate need for recognition from the village. His skills could develop faster as Kushina could train him. He'd also have a better understanding of his Uzumaki heritage earlier, which could shape his identity in a different way.
At first, Naruto and Kushina might start to distance themselves from Minato. They could avoid him and not talk to him as much. As time goes on, the hatred might grow deeper. Naruto could start to oppose Minato in public or in important village matters. Kushina might also try to influence others in the village against Minato.
In many Naruto fanfictions, Minato is often portrayed as an even more brilliant strategist and a loving husband. He might be shown using his Hiraishin no Jutsu in creative ways to protect Kushina. For example, in some stories, he uses it to surprise her with little gifts or to show up just in time when she's in danger.
A fanfiction could center around a family training session. Minato trains Naruto in advanced ninjutsu techniques while Kushina teaches him about the Uzumaki clan's secrets. This would not only strengthen their family bond but also make Naruto an even more powerful ninja.