Izuku Midoriya knew that he could never be a hero. He didn't fully realize this when he had no quirk, neither when the other kids mocked him for being quirkless.
He realized it the first time he killed someone.
He was 10 at the time and he was kidnapped by a cloaked middle aged man who beckoned to follow him in an alley promising to "show him cool merchandising of heroes". That was proven to be less than true when the man pushed him against the ground and, threatening with a knife, began trying to pull his pants down. (Izuku found out years later what the man was trying to do and was thankful that it never escalated that far.) Izuku managed to kick his leg at his crotch causing the man to drop the knife next to him.
Izuku then found himself standing over the man's dead body which had a knife in his neck. Izuku expected horror or remorse to come when he realized that he had killed him. He waited a few minutes more. Absolutely none came. He felt nothing. As if killing the man was nothing more than simply taking a breath.
So he zipped up his pants. Sneaked over to a public bathroom in order to wash of any blood that may have spattered on either him or his clothes (Because even though he felt no remorse he didn't want anyone to freak out about a blood-soaked child.) and went home. When his mother asked what happened to his clothes and why they were so wet he simply said that he accidentally walked through some sprinklers when he wasn't looking.
While waiting for his mother to finish up with dinner he realized he could never become a hero. Because heroes SAVED people and he realized, while looking at his own hands, in curiosity how easily and natural it was for him to kill that man. So he vowed that he would never become a hero. How could he stand up there with All Might when he was like….this?
It was 4 years later when he killed a second time.
He was carrying the burned notebook that Kacchan destroyed. It was nothing new. He told Kacchan that he couldn't become a hero but it seemed as if Kacchan wanted him to avoid the hero life altogether. That was impossible because while he couldn't become a hero he could certainly admire them. Well it wasn't as if he couldn't rewrite what was in the book he did have multiple files on heroes (and villains just in case he was ever confronted by one) so it was no problem. The notebooks were just something to carry around.
Then while he was walking the sludge villain attacked. However before the villain could engulf him with his body he quickly darted out of the way as if he knew he was there. Izuku was mildly surprised at his fast reflexes but that was put off to the side as his full attention was ought before the sludge guy before him.
"Kukuku~ such fast reflexes~. You'll definitely make a good vessel." Then the slime villain lunged at him. That just made it faster for the knife to pierce his eye.
"AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAARRRRRRRRGH!"
Izuku's mind was into instant overdrive while the villain was talking. Noting that the eyes weren't just for show he pulled out the survival knife that he bought sometime after his first assault and threw it with a quick flick of the wrist.
While the villain was flailing around Izuku calmly walked up to him and pulled the knife out of the villain's eye twisting as he did so.
"AAAAAAAAGHGASD" The villain made an attempt to reach out at the boy
Then Izuku plunged it into the other eye and the villain faltered once more screaming in anguish.
Izuku pulled out the knife and darted back away from the villain and watched as the villain flailed trying to feel for the person who incurred his blindness.
The villain heard a flick and a burning, with the smell of smoke in the air. Then the villain realized, as more pain started settling in, that it was he who was burning.
Izuku had bought out a box of matches and made sure to light at least 3 to burn the sludge villain alive and threw them at him.
Izuku watched for a bit as the villain kept screaming and coughing in between.(He threw in 3 more burning matches to make sure that the fire kept going.) When no sound was heard anymore from the villain he walked away back home, once more focused on his objective to rewrite his burned hero notebook. Caring not anymore of the villain that he killed behind him as went home.
All Might went to investigate the smoking tunnel and realizing that it was the slime villain on fire, punched at the fire and the force of the blow blew it all away.
But it was too late.
There was nothing more than ashes on the wind.