That's a spectacular example of how learning styles differ.
Your style is to be results oriented, and anything else confuses you; her style is to be process oriented, and anything else confuses her.
I believe learning styles to be essentially hardwired, or at least fixed at an early age. A good teacher is adept at matching style to student.
Is that a difference in learning style or a difference in how pragmatically long term goals are approached? I won't make any simplistic assumptions about any specific parties here, but my own experience of students who are only interested in the sound (minus interest in the practicalities of getting it) is that they are typically very hard to teach in a way that leads to significant long term progress, unless they are willing to step outside of how they typically like to think, by considering the pragmatic issues that determine control over sound.
Take the first movement of the moonlight sonata. Even the most musical and technically advanced students almost never succeed in truly differentiating between melody and thumb on the octaves. Inspiration never makes any notable difference to this basic ingredient, without which the movement cannot even begin to truly work. They learn to play the other accompaniment notes soft but not to get the thumb voiced softly. I can demonstrate what extreme voicing sounds like, ask them to sing more and whatever else. At the end of it, I still get an inspired pianist who still either fails to bring the melody out at all or who now hits it too hard, still with a heavy thumb underneath.
I never start with the inspirational side any more for the piece or for any other that depends on basic voicing skills. I start by making the student play all lower rh notes staccato and physically connecting solely to the 5th. Once they learn this basic physical feeling, I go on to talk about voicing and sound- in the knowledge that I've shown them the basic means of achieving dynamic differentiation. It's simply wasting time to put all that effort into trying to inspire, only to hear a result that is inspired in their mind, yet not inspiring to hear, due to the basic lack of the means needed to voice. Inspiration also tends to fade faster than improvement of means and quickly goes back to square one. The more I should isolate music from means, in my teaching, the less rewarding it is musically. I either have to be hypercritical and labour points over and over, or simply stop expecting the student to actually achieve any of the things I'm asking for-and simply state them and immediately give up on all but the mildest reflection of what I've described/demonstrated as the musical goal.
Students who are unwilling to get into practicalities tend to hit a wall quickly and don't tend to get to the next stage of development. The sad thing is that they are often VERY musical, but only a certain percentage of that comes through without the basic tools to express themselves with reliability. I was exactly that type of student myself, when growing up- with no interest in issues of technique. I made the most progress in my sound when I became willing to change my supposed "learning style" and got into pragmatics. People don't learn the most by staying in their comfort zone.
PS A friend who is a very advanced pianist and teacher of very advanced students told me she played to Katsaris. Apparently he spent a huge amount of time on how to practise. Everyone needs to be pragmatic and balanced in what they are willing to try, or its a self-imposed handicap against the potential level of progress rather than a "learning style". If someone only wants to enjoy themself, that's fine. If someone wants to better themself to the maximum amount possible, they need to step out of their personal tendencies and be brave enough to explore things that are not necessarily immediately comfortable.