It's less that he finds an argument whose premise is repugnant, and more that he realizes that he doesn't have a good angle of attack for convincing the slavers to not mutilate/kill him at all, but does have one for delaying doing so. I'd argue it's more of a "perfect is the enemy of the good" judgement on his part than a disagreeable argument (After all, Tyrion has gleefully made that clarification to several people before.)