On the simplest level, this old brainteaser is less like an argument than a pun, a noise emitted by the squeaky hinges of human thought. The question confuses us at first by disguising a negative as a positive. It admits that God lacks limits. But it notes that a limit is something, so God is lacking something, and therefore He isn’t perfect. You could say the same thing about flaws. Or feathers. Feathers are something, and they’re something good — God said so, in a roundabout way, in the book of Genesis. But God has no feathers (so far as we know). Therefore He isn’t perfect. One can imagine a boy in seventh grade Confirmation prep class substituting for feathers, “hooters.” “God has no hooters. But hooters are awesome…” and so on.
Still, there are some sober, adult reflections that come to mind when we think about this. As Pope Benedict XVI reiterated in his bomb-throwing address at Regensburg, Catholics believe that God is in fact bound by the laws of logic, which are part of His own very nature. He cannot make a square that is also a circle. Nor can He choose to cease existing, go insane, or make what is intrinsically evil good. Furthermore, He cannot betray His promises or reverse His own decisions. Since He made the souls of men immortal, He cannot decide to unmake them. In other words, an eavesdropper on the inner life of the Most Holy Trinity would never hear a dialog like this one: