Why isn't the American r considered a vowel?

Question

As a native American English speaker from the Northwest, whenever I isolate the r in words like "right" or "rope" it's always /ɚ/, the same as the r in words like "first" or "girl" but the "ir" in first and girl is considered an r-colored vowel, but the r in "right" and "rope" is not considered a vowel

Going through the checklist for vowels:

Open vocal tract - check

Voiced - check

Nucleus of a syllable - while a lot of people would say no I'd say yes

Going back to words like first and girl, you could just as easily write them as "frst" and "grl" and they'd be pronounced the exact same (in American English), the extra letter is purely convention, the r is what's forming the nucleus, and in fact in American shorthand it's quite common to remove the unnecessary letters, in British English I could see the case for r not counting as a vowel since in words like first and girl the nucleus is moreso around the i, being pronounced more like "fest" and "gel"

Just as "turn" can be shorthand-spelled "trn" in American English, but "tun" in British English, and they make the exact same sound as the actual word in their dialect, because in American English the nucleus of the syllable is "r" but in British English the nucleus of the syllable is "u"

So if the American r fulfills all the requirements of a vowel, why isn't it considered one?

Answer 1

Many phonologists do consider "r" in "girl" to be a vowel, I being one. There are many reasons for people to consider it to not be a vowel. First, in "rabbit", nobody considers "r" to be a vowel, only syllabic r is a vowel. Second, "vowel" is a vague term in phonology, given the wide range of terms that can be used to talk about sounds. Vowel may be used to refer purely to degree of constriction, or it may be used to refer to prosodic status – a vowel is a thing in the syllable peak. Classical vowels like [a] satisfy all definitions of vowel and classical consonants like [k] usually satisfy none of the definitions for vowel, except in a few languages there are (controversially, e.g. in Berber) syllabic stops which are syllable peaks.

Also, it is clear that surface syllabic consonants in English can be derived by rule from əC sequences. There is a line of reasoning that says that if you can reduce all instances of [ɹ̩] to /əɹ/ then you should, so surface [bɹ̩d] could then come from /bərd/. This choice depends on a premise that one should minimize the number of underlying segments, a premise that is not universally accepted.

There is a distinction made in phonetics between approximants and other kinds of consonants – American English r is an approximant. Vowels and approximants share the phonetic property of minimal constriction. There are theories of phonological features with a feature "consonantal" which puts most consonants into the consonantal set, and vowels & glides into the non-consonantal set (this does not include /l/). The flapping rule provides evidence that r is in the non-consonantal (vowel-like) set: you get flapping in writer, sitter, barter, murder and not in falter or banter unless you delete the nasal and have a nasalized vowel (bæ̃ɾɹ̩).

Your feeling about r in rope etc. probably comes from "isolating" the consonant. There is a test for vowel status at the beginning of the word – the choice "a, an". I feel confident that you say "a rope" and not "an rope", but "an apple, an urn".