I don't know where it came from, but the "west" at least as I have learned, came up with the idea of "vowels" and "consonants" at some point, and we just go with that classification. But besides linguistic analysis revealing that these categories are in fact fuzzy, and there being all kinds of features behind the production of each sound (voice, airflow/restriction, nasality, etc.), in just thinking about it now, here's how I might break it down if I never learned about this stuff through school (somewhat):
- voice, no voice (s vs. z)
- continuous vs. discrete (s vs. p)
- nose vs. mouth (m vs. s)
No where to be found is the consonant/vowel distinction.
In addition, following question Why r, h, and w aren't vowels, some things could be considered vowels which are consonants, the classification grouping of English, for example, seems arbitrary. So I wouldn't have the "vowel vs. consonant" distinction, how did that even get made in the first place? It seems so arbitrary.
The only way I can think of the reason why vowels might be their own class, is they are voiced, continuous sounds with an open mouth. But z and ʒ are also voiced, continuous sounds, but perhaps with only difference between them is that the airflow is sort of restricted by the tongue. Most vowels and consonants use the tongue in some way to make their sound it seems, so it's not obvious at first thought that categorizing based on this tongue feature would be, well, important or useful. In fact, "i" (ee sound) kind of is like "z", but using the middle/back of the tongue (restricted airflow) instead of the front, so there's that too.
So how did the consonant/vowel distinction arise (tangential question), and what are other classification systems used by other cultures from around the world (main question)?
Maybe y and w are consonants because you treat them as discrete sounds. So y is like i and w is like u, but saying "uuu-one" is not the same as "one" (with a w sound), and "iii-es" is not the same as "yes" (with a y sound). I can't pinpoint the difference here really, but it seems like maybe the length of how I say one vs. the uuu-one, or no, maybe it is that I don't have a slight glottal-stop at the beginning when it's a w, but I sort of have a break/glottal-stop when I start the uuu in uuu-one. It's like my tongue releases from the top of my mouth (closed airflow) when I say "uuu", but doesn't close airflow and hit the top of my mouth at all when I say "w". So it's like the vowels then are things which start with a closed tongue/pipe, and is continuous voice! That is maybe why "errrr" is spelled that way (with an e before r), because it starts with the closed pipe, but "rrr" doesn't have a closed pipe to start. So if it is voiced, continuous, and starts with a closed pipe when stated on its own, it's a vowel? Everything else then is a consonant.