I'll recognize the best entry/entries for each vowel tomorrow. (You can submit more than one.) No dictionaries or computer assistance allowed, and here's a pro tip: Y is a vowel when it makes a vowelly sound.
There's a perfectly good explanation. What is, overwhelmingly, the most likely word to appear directly before "tooths" in a sentence?
The answer is "sweet". As Mr. Gregg put it: "Since I like desserts, I have a 'sweet tooth', and since my wife likes desserts too, the two of us have 'sweet tooths'."
Here are the top six results for "* tooths" in Google Ngram Viewer:
No, I can't explain most of these, but perhaps when dentists throw parties, they play Two Tooths and a Lie.
Congrats to solvers Peter M., Maddy, and Mr. Gregg! Atticus had two great guesses that happened to be wrong: "saber" and "not" (as in "it's not tooths, but teeth"). Leo's guess of "saw" was also quite reasonable (the Sawtooths are one word, however).