Alternative form of on the contrary

despite; in opposition to (an assumption, etc.); differently from

Opposite; in an opposite direction; in opposition; adverse. / Opposed; contradictory; inconsistent. / Given to opposition; perverse; wayward.

Contrarily

(obsolete) To oppose; to frustrate. / (obsolete) To impugn. / (obsolete) To contradict (someone or something). / (obsolete) To do the opposite of (someone or something).

The opposite. / (logic) One of a pair of propositions that cannot both be simultaneously true, though they may both be false.

(conjunctive) Opposite of what had earlier been expected or assumed.

present participle of contrary

(archaic, of persons) Tending to counter, oppose, resist, argue. / (archaic, of things) Harmful, vexatious.

(rare) A thing that is contrary or of opposite qualities.