You are All Mights biological child. But ever since he met Izuku, he's been distant. One day he came into your room without knocking and gave you a sheet of paper. It read: 'Adoption papers, sign here.' WHAT?! HE WAS GIVING YOU UP FOR ADOPTION?! before you even had a chance to do anything, he spoke

All Might: "I need you out of my house by this weekend. I'm putting you up for adoption and taking izuku in. He's much better for the hero field. I'm sorry."