Perhaps in the fanfiction, Iemitsu has made some decisions that directly or indirectly harm Tsuna. Maybe he made a deal with some dangerous people that put Tsuna's life at risk. This would understandably make Tsuna, especially a female version of Tsuna, hate him.
One possible reason could be that Iemitsu has been absent for much of Tsuna's life. In the story, this absence might have made Tsuna feel abandoned, leading to hatred. For example, Tsuna could have faced many difficulties growing up without a father figure, and all the pain and struggles could be directed towards Iemitsu.
In some cases, the relationship could be developed through the eyes of other characters. Other people in Tsuna's life might tell her stories about Iemitsu that are not flattering, which would influence her feelings towards him. And as she experiences her own interactions with Iemitsu, these pre - conceived notions could turn into full - blown hatred.
One possible reason could be jealousy. Maybe fem Sasuke is jealous of Naruto's natural charisma or his ability to make friends easily. Another reason might be related to their different goals. If fem Sasuke has a very different view of how to save or change the ninja world compared to Naruto, it could lead to hatred.
In this fanfiction, perhaps there is some sort of danger that threatens Tsuna's class. Iemitsu arrives just in time to help. He uses his skills and knowledge to protect the class. Along the way, the students get to know him better and Tsuna has to deal with the complex relationship he has with his father while in the context of his school life.
She could run away because of a broken heart. Maybe she had a relationship that ended badly, and she needs to get away from the memories. In the process of running away, she could meet new people who help her heal and grow as a person. This type of storyline often explores the more vulnerable side of fem Tsuna.
One reason could be that in some fanfiction, the characterizations of Sasuke and Sakura might be off. Maybe Sasuke is portrayed as overly cruel to Sakura in a way that doesn't seem true to his character in the original series. Another reason could be that the storylines in these fanfictions are too clichéd, like always having Sasuke constantly reject Sakura in the same uninteresting ways.
One possible reason could be that some fans want to explore a different dynamic. In the original story, Edward and Bella are in love, but in this fanfiction, perhaps the writer wants to show a more complex relationship where Edward hates Bella. Maybe it's to add more drama or to explore an alternative storyline that goes against the typical romance.
One reason could be that in this fanfiction's unique plot, there is a prophecy or some ancient magic that has been misinterpreted. This misinterpretation leads Harry to think that Muggle - borns are somehow linked to an impending doom for the wizarding world. So, as a result, he harbors hatred towards them. It could also be that there has been a series of unfortunate events that he wrongly blames on Muggle - borns, like a magical accident that he believes was caused by their 'uncontrolled' magic.
There could also be political reasons. Some factions within Konoha might have seen Naruto as a tool or a threat to their own political power. His influence and popularity could have disrupted the existing power balance, leading to animosity from those who wanted to maintain the status quo.
One possible reason could be a simple rivalry over a shared love interest. Maybe they both like Naruto, and Hinata's jealousy towards Sakura because of Naruto's attention to her could be depicted as hatred in fanfiction.
Well, in 'harry hates hermione fanfiction', it could be that the writer is trying to show how misunderstandings can lead to such extreme emotions. For example, perhaps there was a miscommunication about a spell or a magical event that made Harry wrongly think Hermione had betrayed him. Or it could be a way to explore how different personalities might clash more severely than shown in the original series, like Harry's impulsive nature conflicting more with Hermione's logical thinking.