This can be difficult to grasp. Your transfer case is working, since you are turning wheels at both the front and the rear axles. Your front and rear axles have the same type of differentials, so forget the front for now and think only of the rear axle.
Imagine a typical front engine, rear drive car. It is considered to be a 2-wheel drive, that is, power is delivered through two (rear) wheels. If you have a limited-slip type differential, when you break traction, both rear tires will spin, whether on wet or dry pavement, or dirt, or snow.
But if you do NOT have some sort of limited-slip or locker diff, you have what is commonly called an open differential. With an open diff, when you break traction, only ONE tire will spin-- the one with the LEAST amount of grip! And this is exactly what is happening with your Jeep.
BTW, all things being equal traction-wise, when one tire on a rear-drive vehicle spins, it will be on the right(passenger) side. I have read why but I can't recall well enough to explain it.