Contrasting

On the other hand,

However,

Yes, but . . .

You may be right, but . . .

I may be wrong, but . . .

Correct me if I'm wrong, but . . .

On the contrary,

(Be careful with this one!)
It appears to be a direct negation of what was just stated,
but it can actually be an emphatic reaffirmation of one's own opinion.

For example: It's not hot. On the contrary, it's cold.

("Not hot" and "cold" mean the same thing.)