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.
Some other students might take advantage of his situation. They could spread rumors or isolate him further, thinking that his hatred for teachers makes him a troublemaker. This would create more conflict in the story.
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.
In the fanfiction, Izuku may start to undermine All Might's actions. He could try to expose any flaws or wrongdoings of All Might. Their relationship goes from one of idolization and guidance to one of opposition. Izuku no longer looks up to All Might and may even try to bring him down. For example, he could spread rumors or try to find evidence against All Might if the story goes in that direction.
Typically, in an 'izuku perfect quirk fanfiction', it starts with Izuku getting the quirk, either through some accident or a special encounter. Then, he has to figure out how to use it. For example, if it's a super strength quirk, he might start by accidentally breaking things. Next, he gets training, often from a mentor like All Might. As he progresses, he faces villains who test his new powers.
In the fanfiction, their relationship could start with a bit of competition. Both are ambitious to be heroes. However, they soon realize that they can achieve more by working together. As kids, they might compete in small challenges like who can run faster or jump higher using their quirks (or in Izuku's case, his physical training). This healthy competition could fuel their growth and transform into a deep - rooted friendship that withstands all the difficulties they face later in their hero careers.
At first, it could be full of hostility. Jirou would see Izuku as a threat to everything she stands for as a hero - in - training. Izuku would see Jirou as just another obstacle in his path. But as time goes on, they might start to understand each other's motives better. For example, if Izuku has a legitimate grievance against the hero society that led him to become a villain, Jirou might start to question her own beliefs about heroes and villains.
Their relationship could develop slowly. At first, Toga might be curious about Izuku because he's so different from the others she's known. Izuku would be cautious but also see that Toga is more than just her villainous reputation. They might start by having small conversations, gradually learning about each other's hopes and fears. As they spend more time together, they could develop a deep bond. Izuku might inspire Toga to be a better person, and Toga could give Izuku the confidence he needs in a world that doesn't believe in the quirkless.
At first, it may show some small frictions between them, which gradually accumulate and turn into hatred. Then, there could be a series of confrontations.
Well, initially, Izuku might be overwhelmed by his new cosmic quirk. But as he trains, he becomes more confident. For example, he could start by accidentally causing small cosmic disruptions and then learn to control them precisely.
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.
In certain fanfictions, the izuku system is a secret. This secrecy can strain his relationships as he has to constantly lie or be evasive about his sudden improvements. But when the truth comes out, it can either lead to a huge rift or a deeper understanding among his friends, depending on how the writer chooses to portray it.