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.
Another reason could be related to their pasts. Perhaps there were some secrets in Minato's past that Kushina discovered and she couldn't forgive. Like if he had some connection to a group or person that Kushina despised, it could turn her feelings for him sour.
Perhaps in this fanfiction, there is some sort of misinformation. For example, someone has spread false rumors about Naruto being a threat to the village, and Minato and Kushina believe it without proper investigation. This could lead to their hatred.
Well, it could be related to Minato's absences. He was often away on important ninja business. Naruto might have felt abandoned by his father, and Kushina, seeing her son suffer in Minato's absence, could start to resent Minato. Also, there might have been some political decisions Minato made that didn't sit well with Kushina. For example, if he made an alliance that she thought was against the values of the village or their family.
One possible reason could be a misunderstanding. Maybe some false information was spread about his parents that made Naruto believe they were bad. For example, if there were rumors that Minato sacrificed the village for some other purpose rather than to save it, Naruto might be angry at him.
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.
Well, it could be that they find out some 'dark secret' about Naruto. Maybe they think he has some sort of uncontrollable power within him that they fear. Or perhaps they are forced to disown him due to political pressure in the village. There could be a group of elders or powerful clans that demand it in order to protect their own interests or maintain the so - called 'balance' in the village.
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.
Maybe in this fanfic, the author wants to create a unique and dark plot. Kushina might be made to hate Naruto due to some kind of misunderstanding. For example, she could be misled to believe that Naruto has some connection to a great evil that she is against.
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 possible reason could be a miscommunication in the fanfiction. Maybe some secrets were kept from Naruto about his parents that made him feel betrayed when he found out, thus leading to hatred.
Perhaps it has to do with a prophecy. They might think that Naruto has a special destiny and that their leaving is a necessary step to set that destiny in motion. They could believe that Naruto needs to grow up on his own to become strong enough to face future challenges.