...a teacher...[needs]...not [to] be trying to impress you....

You mean with his own playing ability? That would be a really, really bad teacher. No teacher I've ever had or worked with or known would ever stoop this low.

Scotch,
I'm not sure if that response is sarcasm so I think that I should elaborate.

The teacher should be able to display the correct flute playing technique and this includes the tempo of the piece. In some instances such as in many of our etudes, the tempo is vital to understanding the melodic line in order that the student can understand the end goal of their work.

I find this particularly poignant recently as I've discovered that one of the local band directors is telling the students to practice the notes of their music slowly and with each note for a full breath. Because of this they are not getting the concept of the musical piece which includes, tonality, rhythm, tone, articulation, phrasing and the basic melodic tune. They really aren't getting his intention of a decent tone or length of time because they aren't taught to form an embouchure in order that they can hold out the notes. So, I think that the teacher needs to push these students a bit with the tempo but not too much. Because (As I'm sure you know) if the teacher pushes the student too fast, then slop is the only product.

I'm not sure if that response is sarcasm so I think that I should elaborate.

It's not sarcasm, and it only concerns the tiny fragment I quoted.