Very well said by adodd81802 and dcstudio. Accordingly, I add to my original comment:
1) The ability to work through a misstep, not a mistake (because all pianists of the 18th and 19th century improvised) is a product of two musical skills. First, as a true performing pianist, dcstudio knows the functional harmony of any piece she plays. Therefore, when something goes awry, she knows instantly how to refer back to the overall harmonic and rhythmic structure of the work.
Recently, Daniel Barenboim was asked how he could remember all of the notes when he performed the Beethoven Sonata cycle. His answer (paraphrasing) was that once he found himself down a wrong alley, then he knew how to find his way back. That is exactly what dcstudio does.
2) Further, my Chair at UT San Antonio is Dr. David Frego, who is chair of the departments of music AND dance. He is an internationally renowned lecturer in Dacroze Eurhytmics.
When I shared with him the philosophy of the modern dance superstar, Suzanne Farrell, he replied that yes he in fact had written his Doctoral Dissertation on just that very subject. Madame Farrell's take on mistakes is that the trick is turn each misstep into a new pathway and interpretation of the overall work.
That is why teaching every student the basic concept of improvisation (like Dalcroze does) is important. You learn how to "go with the flow."
3) Chopin did teach his own compositions. Except, that as the richest piano teacher of all time (750 solid gold francs a week), may of his students were aristocrats who did not consider it important to practice. That is why he kept the metronome on the music stand, just as all the piano teachers of today do, when their student shows up for a lesson with the same attitude.
As further proof, I list a previously posted link to a treatise by Jao Paulo Casarotti, entitled "Chopin The Teacher."
https://www.forte-piano-pianissimo.com/Chopin-the-Teacher.htmlThis elucidates adodd81802's inference that the goal of any true pedagogue is to develop their particular students own individual "voice," as a pianist. When dcstudio and I were at North Texas, everyone of each faculty member's students were carbon copies of their teacher's performance style.
In contrast regarding my great teacher Robert Weaver, I will share with you the following:
For some reason, I sat in on a lesson of one his very promising young students. This kid, who was also a rock and roll bass player, had a left hand of steel (with facility to match).
During the lesson, he made mistakes all over the place, which surprised me, because this kid could play. Afterwards, I asked my teacher why he did not stop him at any point in the lesson and point out any of his mistakes (as he always did with me).
His answer was that: at this point in his learning, the student was developing his own style. And, therefore it was more important that he continue to foster this process, as opposed to the NOTE-PERFECT music conservatory philosophy of interrupting it by pointing out wrong notes.