Why isn't "cet" used with singular feminin nouns that begin with a vowel or mute "h"?

Bonjour Marilyn, Good question! Cette is the feminine demonstrative adjective, no matter what the noun begins with. The adjective "cet" is used for reasons of euphony in front of masculine nouns that begin with a vowel or mute h, simply because it's too difficult to say the hiatus in, for example, "ce homme" or "ce étudiant." Ce becomes cet to make these phrases easier to pronounce: cet homme, cet étudiant. Feminine nouns don't have this problem: cette + vowel / mute h doesn't have that difficult-to-pronounce hiatus, so there's no reason to change the spelling to cet (which is pronounced identically): cette étudiante.