A peace is of the nature of a conquest for then both parties nobly are subdued, and neither party loser.

Ending a fight properly asks both sides to give something up, which is why it feels like defeat to each of them and is not one. A settlement where one party wins outright is not peace but a pause, since the other side is still counting. What makes an agreement hold is precisely that everybody paid something for it.

In any dispute you are trying to close, watch for the urge to win the last point. Offering something real that costs you is usually what makes a resolution stick, and it is cheaper than the argument running for another year.