A breathing specialist (on a podcast, so take that with a grain of salt) said that breathing through your nose uses less overall muscles than through your mouth. This was focused on athletics training. By nose-breathing, the athletes were getting enough oxygen without heaving their chests so much, which uses more energy. The idea was that when you suck in air through your mouth, it works your chest more than is required, so you are wasting effort doing that. I tried it, nose breathing while working out, and it is incredibly difficult. Another guy on the podcast, the presenter, is an ex-rugby player and said he had to tape his mouth shut to be able to try it, and his nose was pouring with snot while jogging because he was not used to it.
I'm not saying it isn't to do with muscles, perhaps a sort of "muscle memory" due to years of breathing through your mouth, but my feeling is there's also a large psychological aspect to it. I nose breath when I remember, but it has to be a conscious effort to sort of clamp my mouth shut. Otherwise I'm :-O like that breathing. I feel like I'm going to suffocate if I nose breathe, but that's not the case of course when I actually force myself to do it.