the Denial-matrix built on logical sand — "why isn't everyone everywhere an alcoholic?…"

The sharpest blade in the critique, and it's genuinely sharp: the meeting's joke — think you're the one-in-a-million who doesn't belong and you definitely belong — is turned by Day into an airtight trap where denial of the Disease is itself proof of the Disease, so that by AA's own logic every featherless biped on earth qualifies, and the whole Belonging-versus-Denial matrix stands on nothing. He is asking Gately, in earnest, to show him the flaw in the reasoning, and the reasoning has no flaw a syllogism could catch — which is exactly the doctrine's most unsettling feature examined from inside.