Did you know that there are two types of headphones – 'open back' and 'closed back' (or 'enclosed back'). This refers to the side of the earpiece away from the ear.
Originally, headphones were all of the closed type until one manufacturer found that it was possible to get a better sound by allowing both sides of the diaphragm to access the open air.
This is logical since enclosing one side makes the diaphragm push and pull against a fixed mass of air that operates like a spring, opposing the movement of the diaphragm.
So open headphones even today generally sound better than closed. The problem comes when you use them for foldback.
Imagine your singer standing in front of the mic wearing a pair of open headphones. Some of the sound of the backing track will leak into the mic, and the singer's voice will too.
At best, the vocal track will be contaminated by other instruments, limiting your mixing options. At worst you might get howl round which,for the singer, might be almost deafeningly loud in the headphones. Needless to say, this would be considered highly unprofessional.
So, closed back headphones it is, even if they don't sound quite so good as the other type. You can always keep a pair of open backs for precision monitoring.
Of course on helicopters, they use closed back 🙂