[atrifix]

Another way of framing this: suppose that player A cooperates in round t-1. Player B notes this. Since in the 1-round game defection strictly dominates cooperation, A can only be rational if he believes that B can be induced to cooperate in round t, which would be irrational. Since B is rational and A knows this, A cannot be rational.

Suppose A cooperates in round t-2. He can only be rational if he believes that by cooperating in round t-2 he can induce B to cooperate in either round t-1 or round t. But cooperating in round t is irrational, and cooperating in round t-1 is either irrational, or comes from the belief that cooperation can induce B to cooperate in round t, so cooperating in round t-2 is irrational, and so on.