They have a hole at the bottom of the handle, furthest away from the mirror end. You can try to balance them on a hook standing upright from that hole, but the slightest bump/vibration/etc will likely cause them to tilt sideways & fall over due to the weight of the rest of it. They’ll rotate around the hook at the hole, and the mirror will wind up underneath the hook due to the weight.

As the other commenter said: physics.