If “pairing off naturally” is anywhere close to how I’d see it, it’s basically hanging out without being squeezed into a predesigned structure. There’s no explicit dating, which takes off some pressure and expectations but at the same time you just have to make an active move if you’re interested or else it’ll look like you’re not. Which is kinda difficult to tackle, actually.
I prefer this “natural” way because I don’t like the implications in the word “date” when asking out a relative stranger. This is not a moral matter but just my social sensibilities.
Pairing
off also tends to imply a man and a woman out of a larger group take a natural liking to each other and begin to talk more, more exclusively and after some time they look pretty obvious.

Not that looking obvious is guarantee, they might just be good friends anyway.
By contrast, dating is comparatively upfront, front-loaded and laden with expectations. It’s already a strong declaration from the start, a lot of decision-making has to happen at the earliest stages, and you’re pressured to decide basing on very little information, including the (in)famous third date.