Antonym for 'preaching to the choir'

You could use the expression it's like talking to a brick wall.

It's an established idiom listed in some dictionaries, and it means that you can't get through to the other person.

Another applicable expression might be teaching a pig to sing, from a quote attributed to Heinlein – especially if you find yourself getting frustrated in your efforts.

Waste one's breath may fit the context: ( from TFD)

• to waste one's time talking; to talk in vain. Don't waste your breath talking to her. She won't listen. You can't persuade me. You're just wasting your breath.

• tell or ask someone something although this will have no effect (often negative) Don't waste your breath. I've already asked her to help and she said no. You'd be wasting your breath reporting it to the police - they never look for stolen bikes.

Most other answers give good idioms specifically for futile conversation. In addition to these, a more general (and perhaps fancier-sounding) phrase that applies here is an exercise in futility. It means nothing will change in spite of the action you're taking.

You might be looking for -

"Being the devil's advocate" - advocating an opposing view (that you may or may not support but the listener firmly does) , often for the sake of argument (opposing for the sake of argument)

The above seems to mean the opposite of the idiom :

"Preaching to the choir"- to make one's case primarily to one's supporters (convincing in vain);