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As Noah became fascinated with William's power to summon mechanical parts and construct a giant mech to aid him in battle, William's heart was filled with the resolve to defeat Noah, who heads realized was a monster by the scent and pressure he released, and due to his strange ability to change appearance, which most likely related to being a half-subhuman of sorts.
Although he had no other thing to prove it, he didn't want to obey Noah anyways, and if he could defeat him in a battle, maybe he could force him to help him.
After all, he believed both were S-Rank, so he still thought he had a chance if he fought with everything he had… but he was just being foolish.
He still believed he was S-Rank even after cleaning an SS-Rank Dungeon because it was not common for anyone to become SS-Rank after clearing an S-Rank Dungeon, many hunters had done this in large parties, and none had become SS-Rank in a single sitting.
Check "The Protagnist's Sister Is Actually the Strongest"!