Minato could be possessive of Naruto in fanfiction due to his guilt. He feels guilty for leaving Naruto alone in the world without his parents. This guilt might manifest as possessiveness, as he wants to protect Naruto from any harm and be the father he never got to be before. He wants to be the only one to guide and care for Naruto, thus showing possessive behavior.
In fanfiction, Minato's possessiveness of Naruto might also stem from his pride. Naruto is his son, and Minato was a great and powerful ninja. He sees so much potential in Naruto that he doesn't want others to influence Naruto in the wrong way. He wants Naruto to follow his ideals and values, and this desire to have Naruto be 'his' in terms of following his path can lead to possessive behavior.
Maybe it's because of the hardships Naruto endured due to Minato's actions. Minato's decision to seal the Nine - Tails in Naruto made him an outcast. In fanfiction, this could be exaggerated to the point where Naruto blames Minato for all his pain and suffering, leading to hatred.
Well, in some fanfictions, Naruto might be faster than Minato because he has access to more powerful forms or has trained in unique ways. For example, if Naruto has mastered a new Sage Mode or a super - enhanced version of his Nine - Tails Chakra Mode, it could give him an edge in speed over Minato.
Well, in the fanfiction world, Minato might be overprotective of fem Naruto because he lost her once. Maybe there was some kind of incident in the past where Naruto was in great danger or even 'died' briefly. This made Minato extremely paranoid about losing her again, so he goes overboard with the protection. He might also be influenced by the fact that as a female in their world, Naruto could face different and perhaps more complex challenges than if she were male, like discrimination or special treatment from certain groups.
One possible reason could be that in the Naruto universe, Naruto has a special connection with the Kyuubi. As a female Kyuubi in fanfiction, she might feel a stronger emotional bond towards Naruto. She may see Naruto as her sole companion or the one who truly understands her, which leads to her possessiveness.
One reason could be that the focus in Minato fanfiction is often on Minato himself and his heroic deeds. Writers might forget that Naruto, as Minato's son, should also have a significant role. To fix it, writers could incorporate more of Naruto's feelings about his father. For example, Naruto could have internal dialogues about how he wishes he had known Minato better or how he tries to live up to his father's legacy.
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.
Well, in some fanfictions, Naruto might be considered stronger because he has access to more powerful forms and jutsus. He might have mastered the Nine - Tails' chakra in a more advanced way than Minato could. Also, Naruto has trained with many powerful shinobi, which could give him an edge in strength compared to Minato.
Often in fanfiction, the resemblance between Naruto and Minato can be for emotional impact. When other characters see Naruto looking like Minato, it can stir up memories and emotions related to Minato. This can create interesting character interactions, like when the older generation sees Naruto and is reminded of Minato. It also adds an extra layer to Naruto's character as he might start to understand more about his father through this physical resemblance, like how people might react to him differently because of it.
In fanfictions, Minato might cry for Naruto due to the missed opportunities. He missed Naruto's childhood, all those years of Naruto being alone. When Minato sees the kind of person Naruto has become despite all the hardships, it can be overwhelming and lead to him crying. He regrets not being there for his son.
In fanfiction, Naruto and Minato often represent a connection between generations. Minato was a great ninja in his time, and Naruto is following in his footsteps. Fanfictions can explore how Naruto lives up to his father's reputation.