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.
There's a fanfic called 'Minato's Return'. In this story, Minato somehow returns and gets to see Naruto's growth. It's really interesting to see how he interacts with Kushina, who is also there in the story, and how they both guide Naruto in new ways. The descriptions of their family bond are heartwarming.
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.
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.
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.
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.
Fanfiction about Naruto being abandoned by Minato and Kushina can also be a way to explore different power - up scenarios. Since he doesn't have the emotional support from his parents, he might be forced to seek power in other ways, which could lead to a Naruto with a very different set of skills and abilities compared to the original series.
One possible fanfiction could be about Minato and Kushina watching over Naruto from the afterlife as he grows into a great ninja. They could be his silent guardians, influencing his decisions in subtle ways.
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.