Why do we care on which side of this particular boundary a particular piece of writing that is near to it lies?

Rhyme?

The woods are lovely, dark and deep,

And I have promises to keep

or

‘Home is the place where, when you have to go there,

They have to take you in.’

One is poetry, one is not? Not hardly.

Rhythm? Maybe, but I prefer "musicality," broadly understood. There should be something evocative in the cadence or the sound. Here's one of my favorite poetry readings. No rhyme, and not exactly, rhythm, but rather cadences and tonality that support and reinforce the semantics.

In short, I suspect that "poetry" is a label best attached post hoc, although most of us know most of it when we see it.