Your first instructor is a fucking idiot. If your backswing is shit, you are going to have to compensate for it somewhere in the downswing and finish.
Your swing starts at how/where you address the ball, grip, stance, hands/arm tension. Then it goes to backswing (how you take away the club, your hands and by default your club face relative to the takeaway, how/where you hinge your wrist (cupped? no no), then to what happens at the top when you initiate your downswing (do your hips get way in front of your hands leading you to being late and pushing/slicing everything because your club face will most likely always be open at impact, etc), then to the downswing (do you drop your hands, do you throw your shoulder over the top, what's the club face/hands when you drop your hands, how much lag, do you cast?, etc), then to finish (how well do you rotate through the ball, is most of your weight on your lead leg, are you early extending, do you flip, etc?). If you conveniently consider any of those parts irrelevant, then your swing isn't going to be a consistent, repetitive thing that you can build on.