Midoriya Izuku stares at him with wide green eyes. "Wow Kachan," he says earnestly, "You're really amazing!" And Katsuki wants to punch him in his stupid, awe filled face.
But he can't do that, because all the little extras are watching, and Katsuki can't exactly discourage complements to his awesomeness. So he just grins and says, "'Course I am! Bet you can't do better."
This isn't a real challenge, not like Katsuki wants. Because Katsuki only learned to skip rocks a few days ago. It's the sort of skill you only learn when your father left the house after work like a good for nothing coward, and you trailed after him because you're not a coward, okay, but being alone with mom is tiring and some days you just can't deal, it's not like you're weak or anything. And so you go trailing after your father like some sort of lost duckling, but not really, because there's a whole lot of other things you could be doing, and you're only following him because you can't be bothered with the big job of being leader to a whole bunch of idiot kids right this minute, and it's not like you can't be alone, it's just... you just... Anyway. And you think maybe you should yell at him, just to prove that running away doesn't do any good, and he always gets this hurt, angry, but mostly defeated look when you get all disrespectful at him, and that should be satisfying or some shit. But you don't, just stand next to him all camaraderie-like and he smiles at you with that dumb "I'm sorry about this" little smile and spends, like, over an hour teaching you to skip rocks in the pond like that makes up for something, even though it doesn't. It really, really doesn't.
But anyway, Izuku doesn't have a father. Just a mom who's the most useless person Katsuki knows of other than his dad, but who Izuku talks about like she's a second All Might. But no dad, so chances are he doesn't know how to skip stones, so this isn't a contest really, not like Katsuki desperately wants, but he figures it can't hurt to frame their interactions as competitions as often as possible, and it's always a good thing for the minions to see him one upping someone.
Sure enough, Izuku picks up the first rock he finds on the bank and throws it at the water. But he doesn't even look disappointed when it goes plop into the water without bouncing once.
The thing about Midoriya Izuku is he could so easily be a rival. Izuku is smart and strong and most importantly, likeable. If Izuku stood up one day and said "Bakugo Katsuki is a loser, I'm not going to play with him anymore," Katsuki doesn't know how many other kids would nod along and follow Izuku instead, but it would be a bunch of them. But Midoriya doesn't do any of that. Just grins at Katsuki all friendly and awe-filled and follows Katsuki's lead. There's a whole lot of kids who think Katsuki's amazing just because Izuku thinks he is, and that really pisses him off.
Katsuki will never really be king of this neighborhood, not rightfully, until he and Izuku fight it out. He doesn't care if it's an actual fight with fists and maybe biting, or it's the more nuanced kind of fighting, where they make comments about each others' talents and try to one up each other until all the other kids agree that one or the other of them is best. But Izuku doesn't seem to understand the social hierarchy, doesn't seem to understand that there is a social hierarchy. He isn't trying to get anything, he's just walking around being encouraging. It's frustrating as hell.
But it's fine, really. It's fine, because he knows that someday this will be his origin story, how he and Izuku were best friends. Because he knows that Izuku wants to be a pro hero one day, wants to be number one, and he knows that he, Katsuki, will one day fight him for that and destroy him. And there's really no better way than that to prove himself.
But then Katsuki gets his quirk and Izuku doesn't. So Katsuki keeps waiting and waiting and it's just like Izuku to hold out on him like this.
The night after Katsuki learns that Izuku is officially quirkless he cries. It's stupid and weak but he does anyway, because Izuku was the only one in their shitty town with even the potential to be second best and now he's nothing at all.
The day after he learns that Izuku is quirkless, when the news has spread to everyone, Katsuki and a bunch of his lackeys beat up some lame-ass kid for no reason except that he feels like it, because that's the sort of thing he knew he couldn't get away with back when Izuku was still someone who mattered and kids were still looking at him with stars in their eyes. He's surprised when Izuku fights him over it, crying like some baby, but fists balled with purpose. He's surprised, but he shouldn't be, because Izuku's always been that sort of idiot. He beats him of course, beats him into the ground with his shiny explosions so bad that he might need a doctor afterward, Katsuki's not sure. But it doesn't matter, cause none of the rest of the idiots care about Izuku anymore, now that he's quirkless. And that does the opposite of make Katsuki feel better.