Perhaps the teachers in the fanfiction are unfair in their treatment of students. They could be showing favoritism towards other students, leaving Izuku feeling neglected and angry towards them.
One possible reason could be that he has had bad experiences with teachers who underestimated him. For example, they might have not recognized his potential and discouraged him from pursuing his dreams, which could lead to his hatred.
Well, his friends might be sympathetic to him. They could try to comfort him and maybe even stand up against the teachers on his behalf. This would strengthen their friendship.
Another aspect could be the general discrimination in the BNHA society. The fact that society is so focused on quirks and those without are often looked down upon might have made Izuku bitter. He could be hating everyone because he sees the society as a whole being corrupt and unkind, not just the individuals who directly wronged him.
One possible reason could be the way the villagers treated him as a child. They ostracized him because he was the host of the Nine - Tails. He was often alone and looked at with fear and disdain, which could have gradually built up his hatred.
One possible reason could be that the council often restricts Naruto's actions. They might see him as a potential threat or a wild card due to his Nine - Tails power. So, Naruto, being a free - spirited person, would naturally hate being controlled by them.
One possible reason could be his feeling of being an outcast. In the original stories, Loki is often treated differently in Asgard due to his nature. He might have felt like he didn't truly belong, which could fuel his hatred. Another reason could be envy. Maybe he saw others in Asgard having things he desired, like power or recognition, and his envy turned into hatred.
It could be that Naruto has a different view of leadership than Sarutobi. Naruto might see Sarutobi's leadership as being too passive or too focused on maintaining the status quo. He, with his more energetic and revolutionary ideas, may resent Sarutobi for not being more progressive in making the village a better place for everyone, including himself.
One possible reason could be a misinformation plot. Maybe in the fanfiction, Naruto has been led to believe that Yondaime had some dark secrets or did something bad to his family that he discovers later in the story.
Perhaps Naruto discovers some dark secrets about Konoha that go against his values. Like if the village has been involved in unethical practices that he can't overlook. This could be things like using underhanded tactics against other villages, which would make Naruto, with his strong sense of justice, turn against Konoha.
Perhaps Naruto feels that the Hokage has been too strict or unfair in dealing with certain situations. Like if the Hokage didn't support Naruto's way of trying to bring peace and unity, which Naruto firmly believes in. This could lead to a growing resentment and eventually hatred.
One possible reason could be a feeling of betrayal. Maybe the Kages made decisions that Naruto thought were against the greater good or the well - being of the ninja world. For example, if they were too focused on protecting their own villages at the expense of others.