3rd POV:
Izuku couldn't believe it... he was trying to wake himself up from the nightmare that he found himself trapped inside of. This had to be a nightmare right because he was given One For All, the second strongest quirk in all of history and yet he was told he was now expelled from his dream school, that he was expelled from UA. Why you might ask was Izuku Midoriya the 9th user of One For All expelled from UA? Well, simply over a pathetic and biased test in Izuku's opinion. Now let's rewind about a year or so, this way you will have more details about everything that has happened.
Izuku Midoriya used to be a quirkless boy who had a few encounters with the number one pro hero All Might. Now, the first encounter didn't end that great as All Might had rejected Izuku's question and told Izuku that he could never become a pro hero and save people as a quirkless person. Then came the second meeting between them which was during the second attack of the sludge villain. In this event, Izuku had discovered the sludge villain attack where his childhood friend (Tormentor) Bakugo Katsuki was being held by the sludge villain since it had escaped All Might's custody when Izuku had grabbed onto his legs. Izuku not knowing that All Might was on-site in his skinny form had heard the heroes talking about waiting for a person with the right quirk and before he even noticed what he was doing he had already run past the police line. Izuku, the quirkless child, was running towards the villain when he threw his backpack and landed a hit on the villain's eye that made the villain loosen his grip on Bakugo which provided air long enough for Bakugo to survive.
Of course, Bakugo being the person he was didn't like the fact that the person he saw as a lower individual was helping the all mightily Bakugo. As such, he was complaining and asking what the hell he was doing. Izuku responded he didn't know and that his body moved on its own but that he looked like he needed help is what Izuku replied with while maintaining a smile. Unkown to Izuku at the time, this had inspired All Might to push past his limit and to go in and save both of them. Izuku thought he was going to die but All Might arrived in time to block the hit and deliver his own.
Izuku was sure he heard All Might say something about being a hypocrite and not acting on what he was teaching as he delivered a texas smash into the villain which caused the air pressure to change. This change in air pressure caused a sudden downpour of rain which resulted in the fires around on the buildings that got stated by Bakugo's frantic use of his quirk. Both of them were taken to the side as they were checked out. Izuku though was getting scolded for what he did while Bakugo was being praised. Izuku wanted to laugh at this situation but didn't. The heroes who were standing around doing nothing were now scolding him and Izuku found it so ironic.
Soon though he was let go and warned not to do it again. As Izuku was walking home, Bakugo had found him and yelled at him that he didn't need to be saved by a quirkless loser like Deku. Izuku just sighed and looked at his notebook in his hands and placed it in his bag. "I guess it's time to figure out what to do with my life," Izuku muttered as he continued walking down the street but it seemed fate was going to change for him that day as this was going to be his second encounter with All Might. "I AM HER---" All Might was saying as he coughed up blood and dropped to his skinny form. Izuku started to freak out since All Might was coughing blood and All Might waved him to stop.
"Hello, Young Midorya... I came here with an apology and an offer." All Might stated talking as he asked Izuku what he was thinking when he had run in to save the boy trapped by the sludge villain. Izuku took a second and shrugged. "I wasn't really thinking... when I heard the heroes talk about waiting for the 'perfect' quirk to handle the situation I found my body already past the police line before my mind realized what was going on. At that point, I had to commit to what I was doing." Izuku stated as he explained what happened. All Might smile widened at the explanation that Izuku gave him and nodded his head. 'Indeed.... he is the one I want. It feels as if One For All is pulling towards him as well when the incident happened since I knew I was already at my limit but I somehow gained enough power to push through my limit.' All Might thought as he listened to Izuku's words.
"Good... good... that settles on what I want to offer you. Young Midoriya, I wanted to apologize to you. I was cruel in my words when I told you never could be a hero because at that moment you were. When everyone else stood by doing nothing you acted." All Might stated and Izuku said he only made it worst and didn't help. "Wrong, it was because of you the quirkless boy had gotten the courage to act that I was inspired to move as well. I was at my limit and I was standing in the crowd. However, due to your actions, I found a new wave of energy to push past my limit and save the day. You Izuku Midoriya are a hero and I believe you can be a pro hero." All Might stated and Izuku started to break down into tears. As Izuku was crying, he was then offered what All Might wanted to offer.
"Young Midoriya, I believe you are the one to inherit my quirk. I want you to inherit my powers!" All Might stated and Izuku froze in confusion and started muttering so many different things out as All Might chopped his head a bit and told him to stop freaking out. "My quirk is unknown to everyone and I always play it off with jokes and changing the topic. However, my quirk is actually called ONE FOR ALL. It is the second most powerful quirk in all of history and I deem you worthy of becoming the next user of my quirk as the 9th user." All Might stated as he explained the details of the quirk though he left out the All For One part to the story. Izuku soon was caught up on what All Might was talking about and accepted the offer without hesitation.
This lead to the 10 months of hell training where Izuku Midoriya under the supervision of All Might started to clean the entire Takoba Municipal Beach Park due to it becoming an illegal dumping ground that the city had failed to clean up. Izuku sadly pushed himself because he wanted to clean the entire beach even outside of the sections that All Might marked out. This resulted in several cases of him collapsing due to exhaustion which he got an ear full for but Izuku did get the benefits from it as well.
During the training, Izuku and All Might also have become much more closers to the point that neither was admitting it but they both saw each other as father and son. Again, neither side was willing to admit it since they were both awkward creatures of social interactions but neither the less they did find a good balance between the two of them. Throughout the training, All Might, would take Izuku out to get ice cream every so often and was starting to learn more of Izuku's life and he had concerns as well about it but kept them to himself since Izuku was still opening up to him more and more.
Now, back to the training itself. Izuku had completed the 10 months of hell and was able to receive One For All. Though, there was a problem! Izuku received the quirk only hours before the actual exam for UA! As such, he had zero time to actually training with the quirk and would be using it during the exam itself with no real guidance except to clench your buttcheeks and yell smash! This lead to the events that he was now dealing with as during the exam he used One For All and blew up the zero pointers. This act gave him enough rescue points to get entry into the hero course but it also meant he caught the eye of his future homeroom teacher Shota Aizawa who was known as the Eraserhead hero. This teacher sadly had a large rate of expulsion and Izuku's act of destroying himself to save the girl did not please him and Aizawa didn't want Izuku Midoriya in the hero course.
Now, we come to the recent day, the first day of the hero course. Everyone was told to put gym uniforms on and to go out to the training field where they started to do a quirk apprehension test. In this test, they were threatened with expulsion if they came in the last place and Izuku would admit he was scared of failing due to having zero time to train with his quirk. He didn't risk training with it during the two months between the exam and the first day due to All Might being out of contact and busy with preparing to teach at UA. As such, Izuku was going to try and learn to control it in a controlled environment where he didn't risk killing someone with a punch he did on the robot in the entrance exam but that decision came to bit him today.
Eraserhead made the threat to expel the last person since someone said the test was going to be fun since they could use their quirks. Eraserhead even gave a speech about heroes were meant to correct the unfairness of the world. However, Izuku found the test itself bias but there wasn't anything he could do about it. Izuku though thought his luck was up when Eraserhead stopped Bakugo from attacking him even though Eraserhead told Izuku that he could never be a hero. However.... it seemed going from a full limb to just a finger wasn't enough for Eraserhead as Izuku came in the last place.
As Izuku stood there he heard the sentence that destroyed him. "Izuku Midoriya, you are hereby expelled from UA. You can go to the principal's office and the Principal will have everything you will need to leave the school. Everyone else needs to go and get changed and go to the classroom to get your schedule." Aizawa-sensei stated as he walked away from the training field. Unkown to Izuku, All Might was standing behind one of the walls and was impressed with Izuku's ability to go from limbs to a finger and thought he was cool and amazing for figuring that out to get the most out of his quirk with limiting the damage but even he was in shock. He knew of Eraserheads expulsion rate and that is why he came outside to watch them.
However, he wasn't prepared himself to watch his protege get expelled because of a damn quirk apprehension test. All Might was honestly confused on how Aizawa could be so cruel to expel Izuku when he's only had the quirk for a few months. Aizawa should know of the truth when the student files had the recent update for his quirk registration in them. As such, Aizawa couldn't claim that he didn't know that Izuku Midoriya only had it for less than two months! However, unknown to All Might was the fact that Aizawa never looks at the student profiles until later on since he doesn't want to judge the students based on the previous teacher's notes and adapt a mindset to the students without seeing them first.
As such, due to things unknown by several parties, the situation wasn't rectified like it could have been and a new path was set before Izuku. Aizawa walked by All Might and asked why he was outside wasting his time spying on a class. All Might wasn't in the mood to talk to Aizawa at all though and gave a general response of he wanted to see his future students. Though All Might did ask why the green-haired student got expelled. All Might got pissed at the answer but didn't let it show. "He isn't fit to be a hero and never will be. He's not more than an arrogant child with a powerful quirk. It's better to kill their dreams now instead of letting them go and them failing later on." Aizawa stated as he walked away and he didn't see All Might tense his hands at that answer. After Aizawa was gone, All Might went to his protege and totally not his son.
"Young Izuku..." All Might called out as he stopped near Izuku. Izuku looked up at All Might and the hero felt a shiver go down his back at the dead look Izuku had in his eyes. "I'm sorry All might... I truly wasn't meant to be a hero it seems. You should never have given me the quirk since I can't get it under control even though I should have tried to during the past two months... I thought it would have been better to do it in a controlled environment instead of risking my and everyone else's lives with how powerful it is.... now I am just a disappointment to the legacy..." Izuku stated as tears rolled down his face. All Might gripped his hands because he was pissed that his protege was reduced to this because of a stupid test that he shouldn't have gotten expelled on. Especially since another student attempted to assault him yet that student is still in the said class!