It's the opposite, as in Is his shoulder hurting?—On the contrary, it's all better, or We thought you didn't like opera.—On the contrary, I love it. This phrase, at first put as by or for or in the contrary, dates from the late 1300s; on has been used since the mid-1800s.
The American Heritage® Idioms Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.
How to use on the contrary in a sentence
On-the contrary, the self is the source of evil, of illusion.Evolution Of The Japanese, Social And Psychic | Sidney L. Gulick