How did model train scales get their letters?

The O gauge was a zero - and so "smaller" than 1 gauge.

HO was "supposed" to be "half-O" but not quite.

In the 1940's there was quite a battle over what scale HO should be, and you'll note that British HO runs on HO tracks but is bigger than US HO.

S was supposed to stand for "standard" - but nobody but Gilbert used it.

Smaller than HO was another fight ... but I never followed it.