The short answer here is that the fitter has things that he or she can do to improve ball flight without changing your swing. Now I am not saying that a fitting is more Important than instruction it’s not but the fitting and instruction should go together seamlessly. In a perfect world your teacher should be fitting you. Let’s say for example you hook the ball. Every manufacturer has a line for people who hook it. In Taylormade (drivers) it would be the plus, in Callaway it would be the triple black diamond, in ping it might be the flat sleeve set up on a G425 LS. If your not properly fit how do you know your in the right model that fits you?
In the old days there was regular, stiff, senior and x stiff. Today in steel shafts there are gram weights from 45-130. There are shafts with steps and without. The job of the club is generally to produce high ball speed, a good fitter can remove a lot of hook or slice with properly for clubs. Ask your teacher if he/she would fit you, no one knows your golf swing better!