Wrong, they can pant and breathe from the nose at the same time. Just as we are able to breathe through our mouth and nose at the same time. In fact the digery do instrument of the aborigines requires it. To be able to play it correctly you have to exhale while breathing in through your nose! Try that one! You are correct however dogs can breathe through their mouth as well as their nose.
Actually dogs breathe better from their mouth. Have you ever tried to hold a dogs mouth shut? They try to get away not only because the don't like it but because they also can't breathe very well. If they couldn't breathe from their mouth they would have a hell of a time breathing and they would not be able to yawn or anything like that
Dogs breath through their nose and mouth easier through their mouth and humans breath through their nose and mouth and can be at ease breathing through the nose with the mouth closed....
And their butt