I haven’t seen anyone really answer the why of it, which is that the industry developed using a floating glass tool called a hydrometer which measures the specific gravity, or density, of liquids.

When you boil the wort to prepare for fermentation, you end up with a sugary liquid that is denser than water or alcohol. Water has a specific gravity of one, and the specific gravity of the wort is increased by everything you dissolved into it. You would float a glass hydrometer in it and lets say you get a reading of 1.055.

After fermentation the yeast has converted much of the sugar to alcohol and decreased the specific gravity. You measure a second time, and multiply the difference by a constant factor to get ABV. let’s say after fermentation you got a reading of 1.015.

1.055 - 1.015 = 0.04
0.04 * 131 = 5.24% ABV

We label with ABV because that was how it was calculated, and remained the same regardless of the quantity served.

There is a similar process for distilling as well. Before these methods people didn’t know the exact amounts, which led to fun things like navy and admiral strength.