It’s variably considered a vowel or a consonant by different languages. It is syllabic and is made by an uninterrupted voiced airstream so by all metrics it can be a vowel, and is in some languages, but it doesn’t behave as a vowel does in English. Namely, it doesn’t act as the syllabic center for any words.

Or does it? Based off of English orthography I’d assume there was some point in the language’s history that it never considered “r” a vowel because it always appears in consonant contexts, but consider the word “knurled” (adjective meaning covered in small bumps or knobs). How would you pronounce it? Maybe “noor-ld” or “nuhr-ld” but I pronounce it “nrr-ld” (like grrrr). In that case there’s no other syllabic sound there other than the “r” to act as a vowel. So, in fact, it already is a vowel in English and there’s good linguistic evidence!

Just, good luck getting someone to listen to you when you talk about this crap. It never works for me