Originally Posted by umd

If you don't involve the arms, all the torque that you can really apply to the pedals is your own body weight. If you pull the bike away from the side where you are pushing the pedal down you can use your arms to generate more torque and therefore more power. This would lean the bike to the right when your left foot is down, and your right foot would therefore be up (12 o'clock). I can't picture how you would do it the other way around.

Edit: I guess in your case the force of the downstroke is just pulling the bike to that side... that's not really what you want.