King Pyrrhus of Epirus won. His army was so depleted by the winning that he is said to have remarked one more victory like it would finish him completely.
Where the term actually comes from
Pyrrhus defeated the Romans at the Battle of Asculum in 279 BC, a real and well documented military campaign, but the cost in soldiers and resources was so severe that the victory left him weaker than a defeat would have. The phrase Pyrrhic victory, still in common use, describes exactly this pattern, a win that costs more than it was worth to win.
Why this shows up in ordinary disagreements
The professional who wins a disagreement completely, leaving the other party visibly overruled with no room to save face, has usually won the specific point and lost something less visible, the willingness of that person to collaborate easily the next ten times it matters. The scoreboard shows a win. The relationship carries the actual cost.
Where to start
Before pushing an argument to a complete and visible win, ask whether the point is worth what a total win will cost in the working relationship afterward.
Conceding a minor point deliberately, or leaving the other person a way to agree without looking defeated, is frequently the cheaper path to the same outcome.
Reading which arguments are actually worth winning outright, versus which are worth a smaller, quieter version of the same win, is a judgment only you can make about a specific relationship. What this gives you is the question worth asking before the argument, not after you have already won it completely.
There is a specific way to leave someone room to agree without it reading as you backing down, and it is worth having ready before your next real disagreement.