People have told me that the only way to win at negotiating is to "be willing to walk away."
So what happens if you've aligned everything perfectly to make your point logically unassailable, and you are willing to walk away? Perhaps you then realize: if you were really willing to walk away, then you didn't care about the outcome anyway.
If that's what it takes to win, then you have a pretty funny definition of winning.
That kind of negotiation is a "win-lose" negotiation: if you're trying to negotiate in a non-compromise way, then there is no "loser" from an exchange. There is only the "right" answer that makes both parties better off.
I think the best negotiations are the ones where everyone cares too much too walk away. That way everyone wins.
But if you're going to believe that, then beware the sort of person who is willing to walk away. They exist, and they'll eat you for lunch. And they won't even care.