So I read up on it. He's right. English is one of the languages that isn't really clear about vowels. Big surprise, right?
Phonetically speaking, vowels are sounds that are made with no constriction in the vocal tract. Basically, by pushing air from your lungs out your mouth and only shaping the sound by the way you move your tongue and lips without ever interrupting the air flow.
Phonologically speaking, vowels are the peak of a syllable.
Now here's the issue with English. We have words like little and castle, where that sound is the peak.
The issue with y and w in English, is that they meet the criteria of non-constricted sound, but they happen at the non-peak of words, too, like in yet and wet.
So we can have non-constricted sounds at the non-peak of the word. Not vowels.
Similarly, we have sounds at the peak of a word that are constricted sounds--also not vowels.
Technically speaking, a sound must match both criteria to be officially designated a vowel sound.
|This picture shows where each sound is produced.