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When we meet them, Katsuki is fawned over by everyone and Izuku is alone. But from the moment they start at UA, suddenly Izuku is the one everyone immediately likes and Katsuki is the one who people avoid (seriously, rewatch the first season if you don't believe me, even Kirishima calls him out until the USJ incident.)

Izuku always moves to save people. It's what makes Katsuki so insecure. From reaching his hand out in the river to being a quirkless kid trying to fight the sludge villain when all the pro's are too scared. Izuku is the definition of heroic. Katsuki has all of the power and skill, but Izuku is the one who always acts like a real hero, and Katsuki is scared that Izuku looks at him and thinks he doesn't measure up. It reinforces his need to try to win every battle by himself. Day 1 at UA he separates from Iida to hunt Deku down and prove to everyone that he's the strongest. But it doesn't work. He loses, and also realizes everyone around him might be just as strong.

Meanwhile, from the start of UA Izuku relies on so many people and they rely on him and he KNOWS it. (He got his quirk from all might, he trusts Uraraka in their first hero training class, he relies on Tsu and Mineta during the USJ incident, he can't get through the calvary battle in the sports festival without his team, he's too injured after his fight with Muscular so Shoji has to carry him, Kacchan wouldn't reach out his hand to him at Kamino so he needs Kirishima to do it, he can't beat Overhaul without Mirio and Nighteye and Eri)

And over the course of the story we see Izuku isolate himself more and more as the responsibilities of holding OFA begin to weigh on him, while Katsuki learns to open up. And things really flip during the cultural festival arc! Katsuki feels immense guilt over Kamino still (and being the reason all the students move into the dorms) BUT he joins the band anyways, and he joins his classmates in doing something for the rest of the school- he's learning to rely on others. MEANWHILE Izuku fights Gentle and does everything he can to keep Eri and Mirio and his classmates smiling, but he does it alone. He can't get help because then the festival will be shut down.

Katsuki has to do remedial coursework to get his hero license, and he's learning the importance of reaching people's hearts, something that comes so naturally to Izuku he barely thinks about it.

Then at Jaku Izuku realizes him being near civilians puts everyone in danger and he goes off by himself again, but Katsuki follows him to help. THEN Katsuki gets stabbed ("Don't try to win this on your own!") for Izuku and Izuku literally runs away from everybody to protect them from AFO. The story has been reinforcing to Izuku that he's a danger to others, that they can rely on him but at a distance, it's safer. That having One For All means he's the only one who can beat Shigaraki and AFO, until-

Izuku is the one who thinks that the others can't keep up. But Kacchan is the one with Class A reaching out to Izuku, Kacchan is the one who lets Iida be the one to catch him, Kacchan has learned to count on others and use team work to save to win.

Even though Izuku comes back to UA and sees that they're all stronger together, and is able to reach out to Aoyama during the traitor reveal, he is still the lynchpin in the plan to defeat ShigAFO. It's still his burden to bear.

And then in the war arc Katsuki is the one in the Coffin in the Sky. Katsuki is the one holding back Shigaraki, with his older classmates and mentors relying on him. And Izuku isn't there because he was kidnapped! Until Izuku gets to them Katsuki is the one who is relied on. (And look at him thanking Edgeshot for saving him for further confirmation he can now graciously accept the help of others).

In his fight against All For One Katsuki literally shouts that its [everyone's] story. And Izuku is also able to rely on others again as he is propelled forward by his entire class to win! They can't do it on their own! They are stronger as a class!

BUT Izuku didn't save Tenko. All Might reassures him that he was saved in his last moments, but he still died (...unless?). His friends were hurt because he was late. He lost his quirk. He's literally back where he began. Except what's different this time? Kacchan has finally accepted Izuku and himself. He wants to be competing and chasing after each other for the rest of their lives. Katsuki leaves the hospital early so they can all be together for the first day of their second year.