Which, unfortunately, does not matter. You don't win arguments with proof, you win with persuasion.

Proofs are but one tool that can be used to persuade the other party, but if the proofs are not clear and quick, usually the other side will feel they are right - "they have won the argument"

On the other hand, a quote like this may well be persuasive to many, and they will feel you are right - "you have won".

This is not "the ends justify the means" - this is understanding how people argue.

There are those that argue on a purely intellectual level; Richard Feynman describes such a conversation with Einstein Oppenheimer and Bohr. But that was noteworthy enough for him to recall it twenty years later!