Yeah, this may not sound intuative at first, but if you try it, it will make more sense. Get a partner to help you if you really want to see it work.
Build an anchor around a tree or some other sturdy post. Wear your harness & tie in to the rope. Clip yourself into the anchor as you would do climbing, such as with the rope & a clove hitch. Attach your belay device to your belay loop & put it on the rope. Stand facing the tree as if it was the rock wall. Have your partner take out some rope from your belay device while you feed it out as if you were belaying. Lets say your right hand is your brake hand. If you want, have your partner wear their harness & clip in to the rope a few yards away from you.
So now simulate them falling on your left. Have your partner take the slack out of the rope & lean back on it to simulate their full weight on your harness. Because you're tied into the anchor you will only turn 90 degrees. The falling climber rotates you away from the wall, your tie in to the anchor prevents you from going past 90. The rope comes out of your belay device, which is on your harness, at an opening of 180 degrees .... out to your left to the climber, & out to your right to your brake hand.
Now switch sides. You'll see how the brake strand & climbers strand both come out of the device together. Now you've no stopping power.
While you're trying the scenario on the left hand side, see how comfortable it is to hold your partner there for 3 minutes while they lean back on the rope. Make sure they really lean back, feel their full weight. What do you do next? If you haven't already, try clipping the belay device carabiner thru your rope tie in knot & belay loop. You'll see an improvement in comfort & it'll make a rescue scenario a little bit easier as you work on the mule knot etc,.