What's the difference in these 3 classes of light armor and why would I ever want hide armor that has a lower armor rating than leather which has a higher armor rating? What's the point of Hide armor then?

Roleplaying, for one. Not having the materials for the next tier up. You like how one looks over the other.

This game doesn't require min-maxing to beat, even on master. So really, its just a matter of appearance. I've been playing through the game wearing Cuffed Steel Gauntlets and Boots, no helm, and Studded Leather armor because thats what looks best for my character concept. And I rarely die or even require health pots.

My new sword and board is loving Fur. Improved via a 30 Smithing skill it's only 2 points below Leather, so I'm happy with it still.