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I assume he lost the exam because once the orca grunts entered the arena he joined the fight and disregarded the rescue operation (it was off screen, but he simply being rude once wouldnt be enough to make him fail the test)
And he is no anti-hero, but the author is trying to sell him as one. All the emotional breakdown he is having now, all his insecurities and jealousy over Deku is all his bad karma thats coming back to bite him in the ass. He has no grown of matured (yet) he is simply discovering that the world doesnt spin around him.