I suggest something.
A person responds with an objection I’d never seriously considered, and which is completely unpersuasive, but which I cannot immediately specify why its unpersuasive.
I’m unhappy because I can’t win the conversation, ie convince the other person they are
Part of what is going on is that the argument being unpersuasive is a statement in relation to my background beliefs, and not about the argument as such. Hence the structure of my response is:
That argument won’t convince anyone skeptical of the position.
Can you modify it to convince someone skeptical of the position?
This is ineffective because the person I’m talking with isn’t skeptical of the claim in the first place. A better response seems to be oriented around trying to get at why we should be skeptical in the first place, and tactically the approach should perhaps be to come from an unexpected conversational direction. Similar to how the unpersuasive argument itself was unexpected.