Why is using opposite rudder and aileron necessary in left turn for coordination?
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.