On the contrary
On the contrary is used to contradict a suggestion made by another speaker.
‘I suppose the movie wasn’t very interesting?’ ‘On the contrary, it was amazing. I loved it.’
‘Good film?’ ‘On the contrary, it was a complete waste of time.’
On the other hand
On the other hand does not mean the same as on the contrary. It is used to give the other side of a question.
Tablet computers are more portable than laptops. On the other hand, laptops are much more useful.
Arranged marriages are quite common in many Asian countries. In the west, on the other hand, they are unusual.