The letter that pretends to be a vowel from a different alphabet
Ancient Greek had its own letter, upsilon, that made a sound English doesn't really have — something between the "oo" in "boot" and the "ee" in "see," said with rounded lips. When Greek words got borrowed into English and written with our alphabet, upsilon became the letter "y." But English speakers couldn't make that in-between sound, so they usually swapped in the short "ih" sound instead — the same vowel sound in "sit," not the long "eye" sound "y" makes in words like "my" or "style."
The rule
When "y" shows up in the middle of a Greek-derived word — not at the end, and not as part of a "y" + silent-e pattern — it almost always represents a short "ih" vowel sound, the same one in "sit" or "gym." "Nymph" isn't pronounced with the long "eye" sound some readers guess from words like "my" — it rhymes with "limpf," not "rhymef." Greek also gave English the "ph" spelling for the /f/ sound (from the Greek letter phi), which is why "nymph" ends in an f-sound despite having no letter f in it at all.
Hear the difference
Reading the "y" as the long "eye" sound (like in "my") instead of short "ih," and reading "ph" as a plain "p" instead of an /f/ sound.
Try it yourself
"Crypt" — an underground burial chamber — is another Greek-derived word with a "y" tucked in the middle. Which pronunciation applies the short-"ih" rule correctly?