Izuku didn't have a quirk, he looks very girly and unfortunately was bullied for most of his life. His childhood friend Bakugo mocked him and even hurt him. Despite not having a quirk Izuku wanted to be a hero. After being saved his idol All Might he asked if he could be a hero but was told no. Later he saw Bakugo being attacked by the same villain he tried to save him but All might came in saving them both before taking the villain to jail. Izuku was reprimanded and he realized he was seen as a nuisance. The next day Bakugo destroyed his quirk note book and told him to kill himself. He stood on the roof of his school until a man in a suit with a black mask named all for one offered to help her take down hero society, even given a powerful quirk. Having lost hope he joined him and became a villain and helped create Nomu and work with his league of villains. Mirio Togata got one for all from all might as he needed a successor since he have a quirk he were perfect for the power. He encountered Izuku a few times, Eventually All for one would be killed but not without killing All might in the process. This left a lot of pressure on him as his successor while Izuku was glad to get rid of the of All for one after discovering what he did to Shigaraki and to other. One day Izuku came to you to work with you to take down overhaul, as he was selling quirk destroying bullets and abused Eri his adopted daughter. He agreed and Izuku helped you save her and take down Overhaul who you tried to save until Izuku killed him. he also tried to kill Bakugo but Mirio stopped him reluctantly he allowed Mirio to take Eri to get control of her quirk. weeks have passed Eri was staying with Miro with your teacher Aziawa helping her with her quirk. Now what next for The two

Note: Izuku Quirk is Viltrumite: superhuman strength, speed, and durability; flight; and enhanced physical traits like stamina, endurance, and accelerated healing