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Bakugo Katsuki only respected the strong. That was a fact. So when a powerful, smart, beautiful, perfect, girl named Ami showed up with Deku one day at the park, he was instantly smitten. She was an otherworldly goddess in his young eyes, the opinion only cemented itself as a fact as he grew older. So he showed his affection the only way he knew how, by acting like a bastard.

So when he told Deku to jump off a roof, he didn’t really mean it, nor did he get the true implications of what would happen if Deku took his advice. And what made it worse was that Ami heard it. She was ridiculously protective of her nephew. (And wasn’t it strange that the useless loser had such a powerhouse in his family?) Hell the only reason she wasn’t homeschooled was so she could protect him. So when she heard Katsuki tell Izuku to kill himself she went into overprotective aunt mode, in turn telling Katsuki to do the same. It broke him, he knew her words weren’t intentional, but they broke him all the same. When he was attacked by the sludge villain, he nearly gave up. To him it was a sign, the same day Ichi Ami - the girl who hung his sun, moon, and stars- tells him to end it all, he gets attacked. But then he remembered the facts of his life. He was strong, the sky is blue, Ami is perfection, and he doesn’t give up.