He Lied
From a young age, Izuku had to hide his quirk. At first, he did it because his dad asked him to, because it was something special that he shared with him. It wasn't too long before he started hiding it in shame. When he finally meets his idol, All Might, Izuku decides he can't live like that anymore. He has to take down his villainous father, All for One, no matter how much it hurts.
Basically, I looked at some fan theories about Dr Tsubasa, All for One, and Izuku and then decided, 'Hey, I want to make a fic!"
The first arc is finished! And it can be read as a standalone fic. But why do that when there's more?
Chapters 1-30: First Arc, pre-UA [COMPLETED]Chapters 31-??: Second Arc, First Year