Why do we use the measurement of proof?

I don't know anything about the American proof, but the (quite interesting) story of British proof can be found in this article: en.wikipedia.org/wiki/Alcohol_proof

Alcoholic beverage 'proof' in the US was simple and arbitrary: 50% alcohol by volume was the US government hard liquor standard for normal quality spirits until about 50 years ago. The abv measures were merely doubled to give a finer gauge by which to give the measure more precision. The old US "Bottled in Bond" designation for a standardised whiskey specified 50% abv, or 100 proof (US), for example, along with several other criteria. The scale was always arbitrary, but one could say that it is an easy to remember and easy to calculate arbitrary scale, with an easy to remember standard gauge number of 100 as a point of reference. Nowadays 'alcohol by volume' is printed alongside proof ratings in the US so that both are usually conspicuously visible on the labels. Are they redundant? Yes.

@Victor top class answer as always from victor. Thanks for the knowledge!