This one does not translate directly from Indonesian. In fact the meaning changes dramatically!
In English if you say on the contrary then you are contrasting 2 debatable claims:
Here we move from the false claim:
..my dog is dangerous.
..to a true claim:
..my dog is very sweet. (i.e. NOT dangerous)
On the other hand(!), if you're comparing two claims and BOTH CLAIMS ARE ALREADY TRUE:
For this kind of truthy contrast, many synonyms are available: in contrast, meanwhile, on the other hand, etc.