Generally, in a straight and level turn, your rudder input matches your stick input. This is different when you are in a climb or at slow speed because of torque, P-factor and precession. When you produce more lift, you produce more drag and vice versa. Therefore, the left wing has more drag on it and the right wing has less.
Net result is that the plane wants to yaw to the left.
You add right rudder and all is right with the world. Same applies in the other direction. You are going slower and therefore the amount of drag being produced is less. Doubling your airspeed with increase your drag fourfold. So any bit of slowing the plane down will result in a big reduction of drag - relatively.