Anyhow now!—we have tracked down the lie with which you're disgusted and which you are drinking to kill your disgust with, Brick. […] This disgust with mendacity is disgust with yourself. (II.124.1366-1369)
Is Brick really trying to kill his disgust by drinking, though? He seems to be simply numbing his disgust. If we follow Big Daddy's logic here, Brick's drinking habit takes a masochistic turn. He drinks both to quell his warring mind and to punish himself for the lies he's fueled and sustained.