Take the lesson because it would be good for someone else with a trained eye to look at your swing. If the pro is any good he will be able to see immediately what the issue is.
With respect to your interpretation of the laws of ball flight one way to hit an intentional fade or draw is to point your club face in the direction of the intended target, grip the club, align yourself to compensate for the flightpath of the ball and then swing normally. The end result is the path of the ball starts out along your foot alignment (and presumably your swing path) and then curves to where the face is aligned. This is how Jack Nicklaus was able to control the ball as well as he did. In other words the pro is 100% correct about club face angle and resulting ball flight path.
What the pro is telling you is that you have unintentionally done the same thing by not releasing the club head at impact. An open club face will result in a fade/cut/slice. One way to tell would be to look at your hand position after impact. Is your bottom hand rotated over the top hand?
You might well be right too about an outside-in swing path being part of the problem but the pro should be able to see that when you hit a few balls during your lesson.
Good Luck!
