To help explain how this works, watch this re-edited  scene so you can see what happens when screen direction gets messed up. In the new version, the guys are going L-R and then R-L and then L-R, etc. While it still is clear this is a chase of some sort, the previously understandable scene becomes something of a jumble. Watch the two clips again, and you’ll see what I mean.

One way to ensure you never run into screen direction problems is to stay on one side of a moving object. That way, your screen direction will stay consistent. This principle is known as the "180 degree rule."