Good question.
The correct answer is you can play it either way. I like your way better than your teacher's.
Now the long explanation why: Baroque and classical trills and mordentes are often played starting in the upper auxiliary note because there are several sources suggesting this is how to play a trill (e.g., the little table J.S. Bach made for W.F. Bach, etc.) A rule that inflexibly does this, though, I think overlooks that particularly during the baroque era the score was very much a starting point (almost like today's method of notating jazz, the score is a mere sketch that the performer is expected to flesh out). Hence my opinion that you can start on the principal note or below if it makes sense musically (for example because you are already coming from the upper auxiliary in the melody, or because you achieve a better melodic line).
Why this detour, you may ask, as you asked about Chopin and not Bach or Scarlatti? Chopin was quite conservative in his taste (even though his pianistic writing is indeed quite revolutionary), and your teacher is not entirely crazy by suggestin gthat you incorporate this, by then anachronic, upper auxiliary note in your mordentes.
In the particular case you ask about, though, you are coming already from teh upper auxiliary note, so even in a baroque piece I would suggest starting on the principal note.
The other trills, which start with a two-note appogiatura (a flat, b flat) are a better candidate for upper auxiliary trills. For those I would say play it one way on Thursdays and another on Saturdays (meaning, be a little improvisatory and play it either way as the inspiration of the moment dictates).
There is a book on Chopin ornamentation, but the author escapes me at the moment. I want to say is Dontington, but I think that's wrong. Bernhard, you there?