I believe that all along he has looked with disdain at the military (even while he was enlisted). What happens then, is that he forgets sometimes that he is supposed to be a concerned vet and he lets his true disdain and contempt slip out. When that happens he has to remind himself to put on his veteran persona and go on the offensive, acting indignant.
What he doesn't understand is that only those idiots who have imbibed of the liberal cool-aid will fall for it. The rest of us see it for what it is.
Well, that and the fact that he was turned down for a student deferment to do graduate work in France (he'd already had four for college). If he didn't sign up, he would have been drafted into the Army, which was doing the heavy lifting in Vietnam at the time. So he enlisted in the Navy -- his bad luck that they decided to shift Navy troops to Vietnam.