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If you were to ask anyone who knew the Midoriyas about the family, they would say they were very close and very private, and that the mother and son duo were lovely, but that it was unfortunate that the son’s father seemed to be nonexistent - either dead or gone or so distant he never showed his face, and how hard it must be for Inko to take care of her son all on her own, with no help.
They would tell you that Izuku must be so responsible and mature for his age - being left alone on his own for as long as he was as often as he seemed to be, and how he seemed perfectly happy doing so. They would tell you that they were sure there must be someone helping out on some way, because Inko’s hours and the way they lived didn’t quite math with her job and how many hours they worked, that there must be some level of generational wealth or external help for her to be as unconcerned with money as she was.
Those closer to them would mention that Midoriya Hisashi was not present, but that Inko still talked about him fondly, no matter how long it must have been since he left them. They would tell you that sometimes Izuku would talk about his dad like he was still there, still raising him, and that it was a special kind of heartbreak to watch this child speak so excitedly and lovingly of a man who didn’t seem to exist in any way that mattered.
If asked directly about Hisashi, the Midoriyas would redirect, simply say he was away a lot, and that after many years they had found a rhythm and balance, and that it worked for them.
To a more insightful person though, they would appear to be not entirely truthful, they would be smiling reassuringly, but with an edge of… something. Something that told of things unsaid.
To most, Midoriya Hisashi was a ghost in society.
To his family, he was much more.
—
Izuku learned early on that there were only a few people who could see his dad.
His mom had always told him about this fact, that he should always come to her first in public to avoid any weird looks or probing questions, but he didn’t truly believe it until two strangers happened to be at exactly the right angle to have a conversation through him, and not appear to even register his existence.
There were other people (some more human looking than others) that seemed to be the same; present in the world, but not part of it, not truly integrated into society like his mom was, and he met them all the time when they came to talk to his dad at home, and he would be allowed to ask them questions about the tails and extra eyes and whatever else was visible on them and not part of standard anatomy, and they would answer with vague language and metaphors he didn’t understand and leave, often out of the window and into the sky.
When he was very small, he assumed it was some strange category of quirks; something that gave people mutations and power but made them imperceptible to others.
When he got older, he started to suspect this wasn’t the case, and that something else was going on. A lot of what he overheard his dad talking about was borderline occult and a lot more spiritual than he would expect of people talking about quirks, scientific as those were.
For a few months he got really worried his dad was trying to start a cult, but when he turned ten, his parents sat him down and explained it to him.
Yokai were real, and his dad was one of them.
That also meant that he was one too. At least partially. And some time in the future, he might end up with the same ears and long tail of his dad.
—
As Izuku grew older, and he continued to have neither the quirk nor the ears and tail he had been hoping for, that would let him chase his dream, he instead turned to learning as much as he could about the yokai that so often visited his home.
It wasn’t too hard; despite not technically being one, he did give off some kind of aura that attracted yokai and marked him as a part of their world. Whether it was because of his parentage, or because of some kind of yokai thing his dad did to him like he did to his mom to mark her, he didn’t know, but it made befriending and learning about them a lot easier.
He had a secret second series of notebooks alongside his hero ones, kept secret and warded by his dad, who despite his unease with his kind’s secrets being noted down by mundane means, was encouraging of his curiosity but still cautious. These were full of drawings and notes on any yokai he met, their powers, likes and sometimes their weaknesses (he learned quickly that many did not like to share those. Yokai were already weaker than they once had been in the modern, quirked world, and to expose themselves further was a risk few were willing to take, even with a child), and he loved them almost more fiercely than his hero notebooks. These were something he could do. Something that didn’t rely on something he didn’t and would never have.
Sometimes, his dad would take him and his mom on trips to mountains and temples and hidden springs, checking in on long-time friends and one-time enemies alike, teaching Izuku the ways of yokai, just in case one day he counted himself among them, and also as something they could do together; a father-son bonding activity that no other pair could do. Those trips were special. They grounded him in a world that felt all his own, where he felt that maybe he could be useful like no-one else - so few humans could see or talk to yokai, and so many of them were under threat from the world moving ceaselessly forward without the knowledge that humanity was not alone in the world. Sometimes they were scary, or dangerous, and sometimes he left feeling shaken and shocked, but they felt like his safe haven.
They made him feel a part of something like he didn’t anywhere else.
He may not have a quirk, a tail or ears, but he still had his connections, and a hope he refused to let die.