Loping catch-up drill

I swim once a week with a small group at the local YMCA. I go on drill/technique day. The other day, our coach had us do what I can only describe as a loping catch-up drill. You push off in a streamline, kick the entire time. Going one way you catch-up, starting with your left arm. After every pair of strokes you pause back in the streamline position, for a couple of kicks, then repeat. On the way back, you start each pair with your right arm. So it's left, right, pause, left, right, pause, etc. On the way back it's right, left, pause, repeat. Unlike a normal catch-up drill where you might normally focus on a Tai Chi slow pull to groove your arm pull, you push it a little. Not a lot, but you do put a little muscle into the pulls. Here's what I don't get. I was much stronger when starting a pair of strokes with my right arm. (I breathe almost exclusively to my right side, though have no particular problem breathing left when doing this drill.) I mean, I was amazed at the difference between the two directions. I'm going to have to try and get someone to shoot a little video of this drill and see what feedback I get. Has anyone else tried a drill like this before? Any idea why I would be so asymmetric strength-wise?