When I was a young student, I got into the habit of breathing on the preparatory beat in most performance situations. This stemmed from years of various directors holding the prep until they maintained the attention and focus of their ensembles, and when the ensemble was ready, the director began the piece.
As a musician this did two things:
1.) It taught me that I had only a set amount of time (i.e. the prep) in which to take in air as the ensemble 'breathed together.'
2.) As I began to take in more air, I was putting an exorbitant amount of tension into my body.
Relaxed Breathing Makes Quality Sound Easier to Produce
Having been a high school band director, I understand from a classroom management setting that these directors were trying to get the ensemble to play the downbeat together, but in doing so were not allowing their musicians to practice relaxed breathing.