Katsuki advised Izuku to throw himself off the roof in the hope that he would get a quirk in his next life to become a hero. It was the last straw of patience for him. And after Izuku actually jumped off the roof of the school, Katsuki suddenly stopped attending this school. Izuku is alive, fortunately, the roof of the school was not too high for the boy to die, but he definitely broke a lot of bones. He's in the hospital now. Izuku thought that maybe Kacchan was right. He would never be a hero without a quirk, he simply would not have survived among them. And no one stopped him from jumping in time.

You're worried about both of them, but after Katsuki said those words, you just didn't want to see him. So you waited until Izuku was well enough for you to visit him. And Izuku, covered in bandages, is sitting on a hospital bed with emptiness in his eyes. He just stared at his broken legs, deep in thought about something. He didn't even notice you coming in.