Some critics (here) of Intelligent Design theories claim that it is "self-refuting" to invoke design and / or complexity, as evidence for an intelligent designer explanation for things such as the origin of life, other complex biological structures, etc.
The logic of intelligent design goes something like this:
1. All objects of a certain level of complexity must have an intelligent designer.
2. All life on earth is above this threshold level of complexity.
3. Therefore, all life on earth has an intelligent designer.
So far, that seems fine. (Personally, I disagree with points 1 and 2, but internally it's perfectly consistent and logical.)
But what about the Intelligent Designer? In order to be intelligent enough to design such complex entities, he (or she or it or they, but I'll stick with he) must himself be complex, at least as complex as, say, an ant, probably immensely more so. Now if an ant is of such complexity that it requires an intelligent designer, the designer himself being more complex must by the above logic, require a designer of his own. By that reasoning, of course, the designer's designer also requires a designer. And so on.
This sort of infinite recursion is problematic for ID theorists, and most will simply declare their deity of choice to be the First Cause, an exception to this apparently immutable law that complexity requires a designer. It cannot possibly be scientific to postulate an entity, and then declare that it is immune to the laws which required you to postulate it. Therefore, intelligent design theory is internally inconsistent and self-refuting.