1/2 beats in 12/8 time sig

For those who read music, and are familiar with 12/8 time signatures:

A note lasting one measure (4 beats) is a dotted whole note.
Splitting one of those in half, we get two dotted half notes (2 beats each).
Splitting one of those in half, we get two dotted quarter notes (1 beat each).
So logically, it seems that splitting a dotted quarter note in half we should get two dotted eighth notes (1/2 beat each), but instead, it’s written (in every 12/8 song I’ve seen) as two eighth notes with a small 2 over them (a couplet). Why is this?

The two eight notes are occupying the time of 3 eight notes, and that’s the rhymic feel that’s notated. I’ve seen 12/8 jazz pieces without couplets.

In 12/8 you essentially have a measure divided into 4 groups of 3 eighth notes. Hence it has a triplet feel to it to begin with. If you want to divide one of your beats in 2 instead of 3, the easiest way is to use 2 eighth notes and just notate it as a couplet. it makes the notes stand out as being outside the feel of the piece, and IMO, it is easier to get your head around than dotted eighth notes.

It’s been a while since I was in high school band, but an expansion on EasyPhil’s answer is that 12/8 time is counted as 4/4, with each beat read as a triplet. In true 4/4 time, a triplet is written as three barred eighth notes with a 3 over the bar, so the symmetrical way to write a beat with 2 half-beats in 12/8 time would be a couplet (as described above).