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..To put it simply, Izuku… doesn’t like his biological father much- to the point of resentment, even, if you look closely. Hizashi Midoriya, Izuku’s father, has been gone for his life since the day he was born ( an overstatement- he left perhaps a week after Izuku was born, but that’s close enough to Izuku’s birth for him to think such ) , something that makes the hero-in-training annoyed . Rarely does his father come home, and Izuku thinks it weird ( it shouldn’t be weird, Izuku tries to think- ) that such an unknown job makes him go out of town long enough to the point that he nor his mom can even contact him.
It peeves him, really– though he partially blames himself for all the physical injuries he’s had and the dangers that’ve strained his mom, he blames his father for also adding his mom’s stress of being the only one to care for him and their home. And even if fathers going abroad due to work reasons ( such as tanshinfunin ) has been commonplace in Japan, it’s still irritating- he’d rather his dad gave more contact than send money or the sparse, fairly occasional letter back home.
In turn, though, maybe others have filled in a paternal spot- take a certain number one hero, who not only precedes Izuku in terms of a very secreted quirk but cares for both his underling students and civilians and all of the world alike. But Izuku holds a tighter bond with him more than others would, almost in a familial sense ( though not overly- maybe, anyways ) , and maybe he’s who fills in the gap.