The argument is really claiming that coding, specifically, is what builds problem-solving skill, not just that some hard class would do it. So the cleanest way to break it is to show that ordinary maths or logic classes work just as well; if a fair, matched comparison finds no extra benefit from coding over those other subjects, then coding was never the special ingredient the argument needed, and the conclusion has nothing left to stand on. None of the other common options — cost, difficulty of teaching, or how much students enjoy it — actually says anything about whether coding uniquely improves problem-solving, so they leave the core claim untouched even if true.