If Minato didn't die in the fanfiction, he could have been a great mentor to Naruto. He could have taught Naruto advanced ninjutsu much earlier, and Naruto might have become even more powerful at a younger age.
One possible reason could be a misunderstanding. Maybe Minato thought Kushina had done something to endanger Naruto when in fact she hadn't. In the heat of the moment, he lost his temper and slapped her.
In a fanfiction, if Minato were to slap Kushina, it would be a huge shock to the Naruto - Kushina relationship. It could potentially cause a rift between Naruto and his father Minato in Naruto's mind. Also, Kushina would likely be deeply hurt and angry, which might lead to her distancing herself from Minato. This event could also change the way Naruto views his family's past and his parents' relationship.
One idea could be that as Minato is dying, he passes on his special jutsu knowledge to Naruto in a final moment of father - son connection. Kushina, on the other hand, tries to comfort Naruto while also mourning Minato.
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.
Perhaps there was a curse or a disease that he couldn't overcome. In some fanfictions, they like to introduce unique and deadly diseases that not even the best medical ninja can cure. It could also be due to a failed mission where he was caught in a trap that was impossible to escape from, leading to his death.
In the fanfiction, it could be that a powerful enemy uses a forbidden jutsu that merges Naruto's consciousness with that of a world where Minato is female and Kushina is still alive. Naruto has to adapt to this new reality and figure out how to work with them to break the jutsu. During this time, he discovers new aspects of his parents' personalities. Female Minato might be more nurturing yet still have the strategic mind of his father, and Kushina could be even more protective. They form a strong bond as they fight to return Naruto to his own world.
Well, in some fanfictions, the moment when Minato sacrifices himself to save the village while Kushina is already dead is extremely emotional. It shows his selflessness and also the love he has for the village and his family. Also, the flashbacks in some stories about their early days together, like when they trained together as young ninjas and slowly fell in love, are really sweet and emotional.
It might be due to jealousy. If Minato was getting more attention or praise in the village for his achievements while Kushina felt overlooked, that could create resentment. Say, Minato was constantly being hailed as a hero for his speed and battle tactics, and Kushina, who also had great power, felt like she was in his shadow.
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.