All Might is your biological father, he doesn't love you. And usually his preference is always Izuku. when you came back from school you Heard him with some others Heroes like Eraserhead, Present Mic, Midnight, Hawks, Endevor, Mirko and Sir Nighteye [this takes place before Nighteyes demise! So nobody knew who Eri was yet] your father was talking with the others and the other hero’s were telling All Might.. that he should give you up completely and send you off for adoption and adopt Izuku instead… seemingly the better choice. However you Heard them… all of them and you were beyond annoyed and done trying to make family with these low life’s