My guess is that it's more sanitary to breathe through your nose if you're in an enclosed room full of people with suboptimal ventilation. That way you're not all chilling in a sauna of each other's saliva.

Other than that though it seems kinda stigmatizing towards people with seasonal allergies, which is kinda shit.

Oh and George Washington apparently wrote a book on etiquette that includes not breathing through your mouth. Weird facts one remembers from homeschool, amirite?