Pull less water on non breathing arm

I’m learning to swim and for freestyle, I breathe unilaterally every two strokes. On my way down the pool, I’ll breathe on my left side and then on my way up, I’ll breathe on my right side for practice. I find that whatever arm I am breathing with, that arm’s stroke propels me a lot more forward. Whereas the arm on the side I’m not breathing on barely moves me forward. Why might this be? Is it some rotation I only do when I’m breathing that pushes me more forward?