How come my teacher's never told me about this simple chord relationship on the guitar?

Yeah, I do ring finger myself. I just tried pinky, and it feels super awkward to me. Depends on your hands I guess, but for me, my hand just smooshes up in a weird position trying to hold down the three strings with my pinky.

I think you mean “Nashville numbering” or the “Nashville number system.” In my experience, it is pretty niche. Most musicians I know are familiar with Roman numeral analysis to some degree, but I’ve never met one who writes up a proper Nashville chord chart like this. It’s clearly used by a lot of (session) musicians working in that industry, but it’s hardly universal.

I have some arthritis in my hands, so it’s easier for me to use the pinky. There are a number of tricks I have to use (probably unconsciously) in order to play without a lot of discomfort, like using four fingers for an aggressive bend.

I have always suspected that “Nashville Numbering System” meant something more profound than numbering the chords of the various degrees of the scale.

To be honest, this stuff gets real complicated real fast when trying to describe to classically trained musicians.
When I say “we’re playing the 4 chord” my wife, a classical pianist, has to pause and think about it. If I start saying “a ii-V-I sounds good because it’s the V of the V” then I am looking at glazed-over eyes.

She is a far better musician than I ever will be, but the slippery combination of “what key are we really in” and chordal relationships baffle her.

There is a bit more to the notation than that. I don’t know the ins and outs of it, but they use various symbols to also indicate rhythms and things like that. Like a chord with a diamond around it means “let it ring out.” A chord with an upward carat and a dot means to choke it. A “-” before a chord number means “minor.” Then there’s notation you may be used to from jazz and the such, like a triangle means “major 7” chord and stuff like that.