I've gone back to read the story again. I think George has lost respect for himself because by enlisting he is going against his own strong principles--how he was raised and everything he really believes about war. At this point, he recognizes that and is just resigned to it.
Interestingly enough his response, "Well, then we'll say I haven't" risks losing her respect anyway. If she were clever enough, she'd catch on that his response indicates that he is saying just the opposite of what he actually means. If he is "collecting" the respect of others because his own is not intact, why throw out such a careless response?