Contrariness is the habit of doing the opposite of what people want or expect, on purpose. A child who says no to every plan, just to say no, is showing contrariness. The word is about a person, not about two ideas being opposite. Though actually, English also uses contrary for “opposite in meaning” (a contrary view); contrariness almost always points at that stubborn, contrary streak in someone. A little old-fashioned, but still used, often when a grown-up talks about a child or a difficult person. It is not a compliment, and not the strongest insult either — more a sigh than a shout.