DekuMaNiC

The name “Kacchan” resounds through Boku no Hero Academia like no other.

It’s physically i­­­­­mpossible for Deku to call him or think of him as anything other than Kacchan

 as @punkbakugo noted here  

spoilers for those who don’t read the manga

In the forest during the villains attack Izuku screams this name as he runs to Mandalay to ask her to use her telepathy.

He is talking to a woman who has never heard this nickname before, he is begging her to give this message to the students of UA (and class B is not familiar with the name as we can infer from Monoma’s “who’s that?”) so that they can protect Katsuki.

“Kacchan?” Mandalay asks confused. But Izuku has to run away from the villains so she has to give that message to the teachers and students, and it’s “Kacchan” that resounds through the forest. Class 1A and Aizawa know who Kacchan is, having heard Izuku call him that countless times, and Katsuki knows that the message comes from Izuku since no one else calls him that.

It doesn’t make sense for Izuku to use his nickname in such a critical moment, but he does. Why? Because he is scared out of his mind, and remembering that saying “Bakugo Katsuki” would serve the purpose better because Mandalay and all the kids would understand who he is talking about is impossible. The reason is that Bakugo Katsuki is “Kacchan” to him. He doesn’t call him that out of habit,

Izuku thinks of him as “Kacchan”.

When we read Izuku’s mind we find “Kacchan”.

And it won’t change in the future since the older Izuku who narrates the story also calls him “Kacchan”.

So when the villains want to take him away and Izuku runs to him, against time, in terrible pain that “They want Kacchan” is all that he can muster.

“Kacchan” is also what Izuku screams when he, quirkless, runs towards the sludge villain to fight him with his bare hands. He doesn’t ask for help, or shout at the villain. He calls out to Kacchan and he does the same thing when they kidnap him because that anguish, the fear of losing him can only find shape as  “Kacchan”.

Izuku has been using this name since kindergarten. And he hasn’t stopped.

And this is important for two reasons.

First, it means that Katsuki never asked him to stop. We know that Katsuki has no qualms about speaking his mind. If he had had a problem with being addressed like that he would have told him and Izuku would have stopped: he is polite and considerate, he wouldn’t embarrass him.

And Katsuki knows that the nickname “Kacchan” is meaningful, that people around them will know that they are childhood friends. That they were and still are close, close enough to use that -chan. And it’s not a problem to him. Todoroki asks him about little Izuku since everybody knows that they are childhood friends and Katsuki does not deny it. Even though his feelings for Izuku, friendship, rivalry, fear are all mixed because of the misunderstanding that originated from his inferiority complex, having people know about the bond between them is not something Katsuki wants to deny or forget himself.

There is no reason why people in high school should know about their friendship if Katsuki didn’t want them to. When they enter UA for the first time they meet people who have no idea about Izuku being born quirkless. It would be so simple to hide the truth from them, to hide the past.

If Katsuki wanted to deny or forget their friendship it would be enough to ask Izuku to stop calling him “Kacchan”.

Kaminari’s “Hey Kacchan” in chapter 163 is him gently pocking fun at him. You can sit there with your arms crossed and a scowl on your face and pretend not to care but you’re here because you have friends and care about their safety, don’t you, Kacchan? Why would he use that nickname if not to tell him that he knows, that everybody knows, that Katsuki can’t deny he has friends. The name “Kacchan” is the proof.

The second reason is that despite his unpleasant traits (as he tells Uraraka in chapter 8 and Katsuki in chapter 119) Izuku can still see Kacchan. The Kacchan who played with him, spent afternoons catching bugs or eating hero chips and getting excited when they found the same All Might card. The same Kacchan who is the coolest kid, the rascal who can do anything. Through the years the things that Izuku started admiring in the playground of their neighbourhood are still brilliant. He does see the bad things, he is not delusional nor blinded by his admiration, and confronts him since the very beginning

It’s the first name we find as the story begins

The first chapter opens on Izuku confronting Katsuki, calling out his friend when he is misbehaving as @kiraelric pointed out here

These two kids idolize All Might, both focus on one side of the number one hero. One is obsessed with victory that society teaches him he can get through his powerful quirk, and the other is obsessed with saving even though nobody expects him to because he doesn’t have a quirk.

This reproachful “Kacchan” is the first sign of the tear between them. At their entrance exam at UA they are two sides of the same coin and in the worst way: Katsuki saved no one, Izuku defeated no one. They need to find the right balance, to fight together and not against each other, to become number one. All Migth himself says it.

He is Kacchan only with Deku

In a chapter title “Kacchan” is used only in Deku vs Kacchan 1 and 2.

The title “Kacchan vs Todoroki” would make sense since the story is narrated from Izuku’s pov and there are multiple occasions where Katsuki is called by nickname as Izuku narrates, but it doesn’t happen. We get “Bakugo vs Todoroki” insted. And “Midoriya vs Todoroki”.

Katsuki is “Kacchan” only when paired with Deku.

Katsuki Bakugo’s hero name

It’s a popular theory in the fandom that “Kacchan” is a possibilty for Katsuki’s hero name and considering that Katsuki’s and Izuku’s past and future as heroes and partners are intertwined, it would make sense for Katsuki to embrace the name that Izuku has been using since they were little.

And the same could be said for the name Deku. Izuku goes as far as using the name Bakugou GAVE to him rather than a made up name of his own creation or even his own birth name as his hero name.

When Uraraka first called Izuku "Deku" he seemed kind of awkward about it. He never had any problem with Bakugou calling him that. So why was he almost ready to stop her? (But he's too nice to tell her not to). She even questions the name and asks if it was in fact a derogatory name. He just fumbles for a bit. The fact is is that he doesn't view it that way. It's the special name that Bakugou gave him and he has always clung to it. In fact, just like Bakugou never told Izuku to stop calling him "Kacchan"...Izuku never told Bakugou to stop calling him "Deku".