"Never hold your breath" is actually a short-cut phrase to tell new students "always leave your airway open." ...
Not exactly. The phrase that was in books and my dive class in the early 1960s was essentially “Never hold your breath on ascent”. Of course students learned a lot about barotrauma during their six class-room sessions.
The complete phrase we learned in my class was “Never hold your breath on ascent or your lungs will explode in your chest and you will die a horrible death”. Totally accurate and made a lasting impression.