> Tell me about other strongly-held positions you’ve changed as the result of a discussion like this one…

Fair point, but if somebody were actually to say that to me during a disagreement, I would assume that they were not acting in good faith.

Now instead of disagreeing about politics or whatever, you're asking a rhetorical question that insinuates "you are unreasonable."

Agreed, it feels like something someone who had never had a conversation with a human being that strongly disagreed with them would write. If it was an introspective question meant to question the framing of trying to convince people through arguments in general, it might be meaningful.

I think it's fair to try to establish if the person you're talking to has an unfalsifiable belief and walk away if you're arguing with a brick wall, but that's definitely not the way to go about it.