Izuku was born with cat ears and tail ears, much like most mutant types that had quirks inborn in them. His eyes were slits and he's been told that by the age of four is when his secondary abilities that comes with the mutant quirk will come. Animal type of quirks were semi uncommon, but his father, from what his mother told him, has a Jaguar quirk which makes him extremely agile and strong and a really good prohero overseas.
He was shown pictures of his dad, he looks so tall and large, well atleast compared to his mom, a large grin showing sharp teeth, proudly wearing his hero costume, his ears and tail shown. Izuku looks at his plain green tail matching to his hair, he wonders if he'll ever get pretty patterns like the one his dad has?
Having a mutant quirk is good in kindergarten because everyone already knows he's bound to get a quirk. He's smaller than kids his age, he's the shortest in class. There is one kid who likes to pick him up and treat him like an actual cat, it would be fine if he didn't randomly pick up Izuku when the greenet is just trying to take a nap or generally disturbing Izuku's life in general.
His name is Katsuki which he calls Kacchan out of spite because it's funny to call someone so scary with such a cute nickname. The blond is thoroughly convinced that Izuku is a real cat and not a human kid. Izuku thinks that even if he's a real cat, he still wouldn't want to be with him, the blond will probably the most horrid cat owner ever.
He keeps disturbing Izuku, screaming at his overly sensitive ears, grabbing his tail, petting his tummy- he doesn't want his tummy pet! He's just trying to take a nap in a comfortable position! Even as a tiny kid, Izuku has learned how to climb up trees to get away from the blond, it all went so good until Katsuki got his quirk and the first thing he learned is to shoot himself up in the air to pull Izuku down from the tree he likes to perch on.
"Stupid cat, don't get yourself stuck up there!"
"I w-wasn't stuck! S-Stop calling me cat my name is Izuku!"
"No, you're cat, you have cat ears and tail." Izuku would protest but Katsuki was already petting him and he knows that Izuku is a sucker for pets.
Aside from that, Katsuki treats him normally, if him trying to make him eat raw fish and cat treats were normal ( they're good food though so who is he to complain ). The blond is unusually gentle with him, even if back then he likes to scream in his sensitive ears he doesn't do that anymore, saying that he doesn't want Izuku to get hearing loss or something. He still likes petting Izuku's tummy ( he's still trying to tell Katsuki that he doesn't like that ).
He's weirdly affectionate, weird as in he shows affection like how humans are to cats, even though they're both small he carries Izuku like a kitten, cradling him, making sure he doesn't escape the classroom, when they're eating and he sees Izuku's bentos are empty, he takes out a small plastic filled with cat food and fills it up. Izuku tries to say to Katsuki that no, he doesn't need to eat cat food but the blond doesn't listen.
He also likes to refill Izuku's water bottle as soon as it goes empty and much to Izuku's chagrin, keeps trying to trim his claws- like he's Izuku's owner or something ( he is not ), and trying to brush his teeth- Izuku knows how to brush his teeth by himself! Everyone thinks it's funny that Katsuki keeps treating him like a pet, Izuku doesn't think it's funny and thinks Katsuki does know but he's just making fun of Izuku for the heck of it. Even his mom thinks it's cute, it wasn't!
"I got you a box." Katsuki says, putting it down and kicking Izuku's chair away, replacing it, Izuku easily sits himself inside of it, Katsuki pets him as he does. Katsuki sits at the front of the day care while Izuku prefers to sit on the back, so Katsuki stands up from time to time just to check on him, making sure that his food bowl is full and that his water is fresh and cold.
Izuku wants to tell him that if Katsuki's gonna do this, he might want to make a schedule instead of just refilling it every time it goes empty.
"Katsu-kun really likes you, doesn't he, Izuku-kun?" A classmate of his said.
"He's making fun of me..." Izuku pouts.
"Eh? You're the only person he's nice to though. He's mean to everyone else."
"He is?" His classmate nods.
"Katsu-kun won't even share his water with us but he refills yours when he thinks it's not cold enough."
Like pet owners, Katsuki gets jealous when Izuku likes being pet by someone else, or when someone tries to hurt Izuku or tries to pick him up like Katsuki does. Usually blowing them up, Izuku likes that he doesn't have to deal with bullies ( or anyone else really ) but the way Katsuki coddles him after everytime is kind of irritating.
"Can't you atleast call me by a name instead of just calling me cat?" Izuku asks, "My name is Izuku."
"That's not my name-"
"Oi Deku, I got you a thing." Katsuki says, pulling out a collar, "my mom got it for me, you can have it."
Izuku doesn't like it but doesn't protest when Katsuki puts the red collar on him before he picks up Izuku and hugs him.
"There you go, new collar for you."
"I don't like it." Izuku openly states, Katsuki ignores his comment before gently putting Izuku down to the ground again and then goes to pet Izuku all over again.
"I'm not a literal cat."