There has been a social stigma against breathing through your mouth in the UK for as long as I can remember, with it being associated with negative qualities like being undisciplined, unathletic, dimwitted, along with it being considered an impolite thing to do.

I doubt this was part of the curriculum, but in fitness classes at school we were told that breathing through your nose with your tongue pressed against the roof of your mouth helps develop your face/jaw and that breathing through your nose moistens the air and helps filter it. We were also told that it's not necessary to breath through your mouth when you're out of breath as you won't get or don't need more oxygen and that you risk hyperventilating this way, instead we were told that you should breath using your diaphragm to help mix the air in the lungs and that you should hold the breath for about as long as you inhale/exhale if you can help it. This sort of breathing exercise seems pretty common in any fitness/exercise related guide I've seen too.

As far as other countries/cultures go, any country that has a strong yoga/meditative culture likely considers breathing through your mouth to be bad too, but this is just speculation on my part. Pranayama is thousands of years old for instance and is primarily concerned with controlling and reducing your breathing, which is hard to do if you're not breathing through the nose.