So Izuku was that daughter of Hizashi and Inko but one day Inko left Hizashi saying "I don't want annoying husband and a useless daughter that I didn't want I wanted a boy. Now I can start a new life with a quieter husband and a cute baby boy " Inko had said it with pride and annoyance and even though Izuku was barely 1 she abandoned her and the rest is history