Disclaimer: I do not own My Hero Academia or Superman, all rights go to their respective owners.
Izuku and Katsuki became friends nearly instantly, while their first words may have both been "Kaa-Chan" their second words were respectively "Kacchan" and "Izu". They would be brought together to be playmates nearly daily, up until the point they both became four years old.
Katuski manifested his quirk at the early age of three, his quirk is "Explosion" which allows him to secrete a nitroglycerin-like sweat from his palms and allows him to detonate the sweat at will causing explosions, these explosions became more powerful the more Katuski sweats.
He manifested his quirk at preschool and was praised constantly for it, this has started an "I am the best" mentality which fed his ego massively even as a child making him slowly more and more prideful. Izuku's quirk is assumed to be having much stronger skin, its limits are untested as he is currently a child, which means any powers he has would be weaker anyways as quirks/superpowers grow stronger the older you get, this is causing Katsuki to believe he is better than even Izuku, his childhood friend due to his amazing quirk and the ego he is gaining.
Katsuki's new attitude towards Izuku caused him to start drifting away from Izuku even going so far as to create a new nickname for him "Deku" meaning "The one who can't achieve/do anything" after a few days of Izuku not leaving "Kacchan" alone. This has caused Izuku to be bullied by a few of his classmates for having a "useless" quirk, the popularity of Katsuki and everyone else trying to become Katsuki's friend due to his quirk. Around this time All-Might had his hero debut gaining a massive amount of fans, including Izuku Midoriya and Katsuki Bakugo, although Katsuki just wanted to defeat him.
At the age of 5 Izuku had enough of not being able to fight back whenever he was bullied and chose to start learning martial arts, he was introduced to a Chinese martial artist through Masaru Bakugo after convincing his mother Inko to help him find a teacher.
The martial artist, named Chao Fan who had moved to Japan in hopes of finding someone to pass his martial arts onto, he was unable to find any students in China who were worthwhile, while there were many students with quirks perfect for Kung Fu, with a lot of talent to boot, they did not have any dedication towards the art of Kung Fu and his own unique style of using punches, aerodynamics and kicks, coupled with his own "Augmentation" quirk which gave him Super strength and Speed, instead they just wanted to use his style to become heroes, not that he had anything against heroes, but the potential students he has met only wanted the fame and fortune involved with being a hero.
Chao Fan moved to Japan in hopes of being able to finally pass down his martial arts as he was getting older and leaving his prime, he also did not want the style he poured his heart and soul into to disappear, he would be forced to however as he absolutely refused to see his style used by anyone not fully invested in it. When he met Izuku, Chao Fan did not think much of him, he was a child with a simple mutant type quirk that only hardened his skin, while this could mean that Izuku would have much better defense than his peers it did not fit his style much as it required blinding speed and strength, something Chao Fan himself only achieved in this age of quirks with his own "Augmentation" quirk. Izuku even begged him to accept him as a disciple, or at least introduce him to someone who will, but his martial arts just did not seem to fit Izuku. That is, until he discovered Izuku's unnatural strength and speed which made him much faster and stronger than his own peers, most likely due to his quirk, but that was limited by his timid personality which did not allow him to make full use of it.
Chao Fan has found multiple people with quirks that would allow them to make better use of his style and was thinking of refusing teaching Izuku his style due to his weaker personality, which usually means having a weaker will. when he saw Izuku defending another 4 year old child from Bakugo and his three friends, 'Finally a student with the heart of a hero, I'll accept him as my student as long as he persists and shows enough investment into his martial arts for the right reasons, after looking through most parts of China, I finally find someone who seems worthy of learning my martial arts style, his quirk is fitting, he would have defense, strength and speed'.
"Stop" says Chao Fan, "What did you say, Old Man?" Says Bakugo, "I said stop, now leave before I am forced to protect this child, Izuku from you" "As if you could, old man, you must be that Martial arts teacher my dad talked about, what could this loser do that I cant? My quirk allows me to create his explosions, all his does is make his skin harder" "It's simple and I pity you for not being able to notice it Katsuki, he has the heart of a true hero and an amazing human being, he protected another child from you and your friend's bullying, even risking himself in the process, something heroes have to do every single day." Bakugo gets angry, uses his quirk in the air then walks away feeling heated and bitter, but at the same time deep in thought. "Really? I can be a hero?" Says Izuku, sniffling. "Yes, young child, You can be a hero, Come to my dojo every day after school from now on, I accept you as my student." "Thank you, Sensei!"
Chao Fan walks away feeling satisfied by his new student, 'Even with his weak personality, he has a strong will and a hero's spirit, even if he doesn't show enough investment in my martial arts style "The Flowing Dragon Style" he will be a great hero someday, i'm sure of it. I named my style "The Flowing Dragon Style" due to all of the moves and the strength, speed and acrobatics showing traits of those of a dragon. Even the basics should help him with creating his own style, if he shows enough investment I shall make him my successor and inheritor of my martial arts style.'
Thanks for reading this novel, i'm very surprised and pleased with the amount of attention it has gotten, I will try to upload a chapter daily/every two days and increase the amount of words per chapter. I chose the martial art Kung Fu because I want to make use of Izuku's future strength, speed and flight powers. A martial art style which requires him to grapple his opponent and use their own strength against them wouldn't work because it wouldn't suit him. Thanks to Truedawn for writing tips.