It could be that in an alternate universe within the fanfic, Naruto's parents didn't die. But they had to give him up for some reason. As Naruto grows up and becomes a hero, they see his journey from afar. They regret their decision deeply because they realize they missed out on his life and all the things they could have done as a family.
He might be angry at first. Naruto has grown up alone and had to fight for acceptance. So when his parents say they regret abandoning him, he could lash out, saying it's too late. After all, he has already faced so much without them.
Maybe it's because she sees Naruto's strength and how he has overcome so many difficulties despite her absence. She realizes that if she had been there, she could have made his journey easier. Also, she might regret not being able to watch Naruto grow up, miss his first steps, first words, and all those precious moments that a mother should be a part of.
One possible reason could be a curse. Maybe some enemy put a curse on Naruto's parents that made them forget about him. It could be a way to get back at them by targeting their most precious thing, which is their son.
Maybe they were under some kind of curse or dark magic that made them fear they would harm Naruto if they were close to him.
One possible plotline could be that Minato and Kushina raise Naruto as a normal child in Konoha. Naruto would grow up with their love and guidance, which would significantly change his personality. He might be more confident from the start and not have that intense need to prove himself. Also, Minato could train Naruto personally, and Naruto might inherit his father's skills much earlier, leading to different adventures and battles in the ninja world.
In this fanfiction, it could be that Naruto's parents were under some sort of mind - control. Some evil entity could have taken over their minds and made them feel hatred towards Naruto. Also, it might be related to a family secret or feud. There could be something in the family's past that made them believe Naruto was a stain on their family name, even though Naruto himself was innocent. It could also be a case of false information being spread around the village which made his parents believe lies about him.
One possible reason could be that Naruto has some sort of power within him that they fear. Maybe it's a power that they don't understand and think could be dangerous, so they hate him out of fear.
Maybe she was forced to for some dark reason. Perhaps there was a threat to Naruto's life if she stayed, and she thought leaving was the only way to protect him.
One possibility is that Naruto realizes Sakura has feelings for Sasuke that he can't change, so he decides to focus on his own ninja journey alone and leaves her to figure out her relationship with Sasuke. He might feel that his presence is only causing confusion or getting in the way of her true feelings.
One possible scenario could be Naruto exploring new jutsu by experimenting on his own chakra. Maybe he tries to combine different elemental chakra within himself in unorthodox ways to create a super powerful and unique jutsu. Another could be related to his physical endurance. He might experiment with training methods that push his body to the limit, like enduring extreme pain or fasting for long periods while still trying to perform at his best in combat simulations.