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This is a fascinating letter. LW is signalling throughout that he is not who and what he says he is. First of all, he signs off as "Amused," when it is hard to see what is amusing about the scenario he paints. Obviously the "debate" in LW's household has been more than merely philosophical, and it isn't about clothing styles, either.
What snappy dresser LW wants us to see as "amusing" is that his frumpy wife is upset, though he carefully obscures just exactly why. Is there more to the tale of just what happened when the (single, for him) drink came over and LW waved cheerily to the gay guys and suggested to his wife that they join them? Did LW do something there to upset his wife?
What a stroke of genius to make it all her fault! LW has been practicing a long time--maybe this is another aspect to the amusing debates he and his wife have to pass the time, probably with increasing intensity.