(A pedant writes...) This is an old chestnut, and a silly and inaccurate one, based on the facile misconception that the only vowels in English are AEIO and U. Y in English is a vowel more often than not, and the W in words taken from Welsh is a standard vowel in that language. Even R can be a vowel in Srbian! Without a vowel, a word would be pretty well unpronounceable, apart from interjections such as Psst!, Grrr! and Hrrmph!
I was taught in the 1940s that a vowel was any letter that could be pronounced without any part of the mouth; i.e. lips, teeth or tongue , touching. Given this criterion, Y is a vowel.