When you don’t know what to say — just say nothing.
When you run out of things to say or have reached an impasse in the negotiations, nothing says you have to keep talking.
In these times where personal philosophies and political beliefs have seemed to divide even those closest of friends and family, there are going to be times where both sides have their teeth clamped down so firmly on their point of view that they won’t allow for even a sliver of acknowledgement from the other side. When you reach a point in conversation like this, I think the smart move is to stop the escalation.
When your conversation changes from an intelligent exchange of ideas where both sides are open and willing to be convinced of the value in the other person’s viewpoint, and perhaps come to an agreement to take a little bit from the other side and merge it into their own, and it devolves into what is essentially a ping-pong match of “yes it is” vs. “no it isn’t” — there is no value in continuing the conversation (because it ceased to be one).
The only thing left at this point is to aggravating one another and make the flames of those burning bridges grow bigger and brighter. If you are aware enough to realize what’s happening and take steps to help deescalate the conversation-turned-argument before the bridge gets set alight, you leave open the possibility of returning to this debate when both of you have cooled down.
Stop talking away and start walking away before one of you takes it too far.