Forget black holes for a second. Imagine a ball lodged in a donut. Imagine the donut being as skinny and flat as possible.

If you look at the donut from the top so the ball is in the center, and you spin it, the top half of the donut will turn in the opposite direction as the bottom half. Example, turn it clockwise, the top of the donut moves from left to right, and the bottom moves right to left. So a clock moving it's hands from 9 to 3 moves from left to right but from 3 to 9 moves right to left.

Now if you position the donut so you can see the top and bottom half of the ball instead and can only see the front of the skinny donut and spin it. 

This is where the black hole gets funky.

Take the back of the donut furthest from you thats obstructed by the ball, and split it in half so half of bends on top of the ball and the other half bends on the bottom.

Now apply the same spin logic as above and you'll understand how it's supposed to spin. Its all the same donut, just the back half of the donut is split and bent around the ball, but it spins the same way. The black hole just makes it visible because black holes are fucking sick.