The riddle
What Do You Call a Pile of Cats?
Mountain and meow, sound by sound
Wiktionary gives mountain as /ˈmaʊn.tɪn/ in British English and meow as /miˈaʊ/. Meow starts with an m and slides into the same "ow" vowel that opens mountain. Two things differ. Meow has a brief y-like glide after the m, and mountain has an n after the vowel that meow-tain does not. The two words are close but not the same, so the answer is better heard than read.
The real word for a group
English does have a noun for a group of cats. Wiktionary defines clowder as a group of cats or other small felines, lists clutter and glaring as synonyms, and traces the word to a variant of clutter recorded since 1801. A 1984 New York Times column, quoted by Wiktionary, uses the phrase "a clowder of cats". A pile is something else: it describes how the cats are lying, not how many there are.
A collective word of its own
Mountain is itself a kind of group word. Wiktionary traces it through Anglo-Norman to Early Medieval Latin montānia, described as a collective based on the Latin word for a mountain.
Where meow comes from
Meow imitates the sound it names. Wiktionary calls it an alteration of the earlier mew and says it came into widespread use in the 19th century, mostly replacing mew. The entry suggests the change may have happened because mew had stopped sounding much like a cat as pronunciation shifted.