i like to believe that Izuku still believes in santa, and nobody knows but Katsuki.
Inko would just assume he figured it out when he was like 8, but Izuku didn't really have any friends so nobody else told him.
Katsuki still isnt friends with Izuku, still hates him, but he only hates him in the way you hate your annoying younger cousin. he pisses you off, but you're family. so when they're 9, in the weeks leading up to christmas, Katsuki sees Izuku crying his eyes out, and since he doesnt have any injuries, he gets curious as to why and asks him whats up.
Izuku proceeds to cry about how hes afraid santa isnt gonna come this year because theres been no elf around his house (Inko, assuming Izuku was too old to give a shit, stopped doing that sort of stuff).
Katsukis known santa wasnt real for a couple years now, but again, despite them being the same age, hes got that annoying younger cousin relationship with Izuku, so instinctively he feels like hes gotta keep the christmas magic alive.
SOMEHOW, he finds himself actually sneaking into Izukus house to move the fucking elf around and actually put gifts under the tree from 'santa'. Inko assumes its Izuku doing it, so doesnt say anything, and Izukus just happy santa didnt abandon him.
except as they get older, Izuku still doesn't figure out santa isnt real. Katsuki refuses to crush his spirit, so and again and again, he ends up begrudgingly being santa for him. hes broken into Izukus house so many fucking times at this point. after year 2 he gave up on actually eating the cookies and milk that Izuku leaves out so he just throws them in a bush on the way home. he is absolutely fucking PISSED that he has to keep doing this every year, but hes kinda gotten himself into this situation where he has no choice because he refuses to crush Izukus dreams after putting this much effort into keeping them alive.
hes done this since age 9. by the time they're in UA, its kinda instinctual to act as if santa is real infront of Izuku. the rest of the class does NOT get the memo. at one point a bunch of them start trading stories of when their parents told them santa wasn't real, and Izuku walked in. Katsuki started playing bass boosted music through his phone on full volume to make sure he didn't hear.
Izuku keeps making comments about how santas real, but people just laugh it off as a joke. the only thing that confuses them is that Katsuki keeps fully backing up everything he says.
like a week before the first christmas they all have to spend at the dorms, they all figure out Izuku thinks its real when Katsuki ISNT in the room, and they proceed to try and gently break the news to him. he cries for an hour.
but eventually he calms down and they start talking about how he never figured it out, and about how all the santa stuff that parents usually do when their children are really young, just... never stopped.
its at this point Katsuki walks in, sits down, listens to the conversation, and freezes. because fuck.
they're all like 'so if it wasn't your mom who was giving you gifts from santa, who was it?' and Katsuki just sinks down in his chair silently.
Izuku, remembering that time Katsuki tried to get him to leave out protein bars instead of cookies 'incase santa was training to be a hero' when they were 14:
Izuku, remembering how Katsuki was the only person ever to back him up about santa being real:
Izuku, remembering that time Katsuki told him he needed to get better security because it was really easy to break into his house:
Izuku: *slowly turns to stare at Katsuki*
Katsuki, internally: shitshitshitshitshitshitshit-
Katsuki: YOU WOULDN'T STOP FUCKING CRYING I DIDN'T KNOW WHAT ELSE TO DO
Kirishima: bro have you really been pretending to be santa since you were 9