Why is using opposite rudder and aileron necessary in left turn for coordination? This question goes against everything I've read or heard with the exception of a suggestion from my CFI in my last flight lesson, so I was hoping to get some clarification:

During a left turn into our crosswind leg my instructor informed me that I shouldn't be using so much left rudder, and in fact, might even need to use some right rudder to stay coordinated due to the left turning tendencies of the plane. I could somewhat understand given that I definitely noticed a tendency for the plane to roll more when turning left than right, but still I would think the antidote for that would just be less left rudder, not opposite rudder.

This does not make sense to me. In what situations would I need to do this? I was still able to perform my turns just fine with slight right rudder on my left turns, but I would like to understand this more.

FYI - I'm flying a Piper Cherokee 140 (PA-28-140)
First and foremost you should always be looking at the turn coordinator to see what is going on and applying rudder as necessary.

In your specific case (if we want to discuss the physics), basically what your instructor is saying is that you are using the ailerons to bank (turn) the plane and the rudder to counteract the propeller's yawing moment. The rudder is simply counteracting the Adverse Yaw: the inputs will change depending on how steeply you are banking. If opposite rudder is called for on your ball, then step on it. 

Perhaps more importantly, what your instructor is actually stressing is during your crosswind, base and final turns you should really be paying attention to staying coordinated. A great deal of Stall -> Spin -> Crashes happen in the pattern as planes slow down and dirty up, thus it's extremely important in the pattern to watch your speed and your turn coordination.