It happened a lot in our nation's history that folks would have relatively simple kitchens not equipped with scales or even a set of measuring cups, so eating vessels and utensils would be used. A lot of staple American baked goods like biscuits are really more about feeling the consistency of the dough than sticking to a recipe anyway, so laboratory precision is not necessary.

At some point the cup got codified as half a pint, or 8 fluid ounces, or slightly under 0.125L. A tablespoon is 1/2 of a fluid ounce and thus 1/16th of a cup. A teaspoon is 1/3 of a tablespoon.

It works out that tea- and tablespoons are ~ 4.928 and 14.786 mL respectively. The medicine industry, which actually does everything in metric and has for decades now, often writes dosing instructions in metric tea- or tablespoons of 5mL and 15mL respectively. For example, my bottle of Listerine mouthwash says in its instructions "swish 10mL (2 teapoonfuls) between your teeth for 30 seconds..."

Believe it or not we also know how long an inch is, too.

I just realized 59.15 ml is 1/4 of a cup while 1 cup is 239.59 ml