Rationality and logic seem to be connected. However, any limited body of knowledge allows only a limited (though possibly infinite) realm of statements to be derived from it. Any finite body of knowledge that is used in a logical way has a limited reach. In order to create new knowledge, we have to use processes of experimentation, of trial and error. We have to make jumps in our thoughts that are not justifiable by any logic and might turn out to be wrong later on. If our thinking is to expand beyond what we know already, we have to embrace our fallibility. Creativity and innovation are inevitably connected to accidental discovery and the possibility of error. Rationality without error is sterile.
People believing in intelligent design seem to reject the idea of evolution because in evolution, there is a place for accident and chance. They do not like to think of themselves as a product of a process involving accidental events. They want to be the product of rationality. But this idea involves a mistaken idea of what rationality is. The creator these people imagine is totally infallible and rational in the logical sense. The creator is imagined to be omniscient and thus infallible. But how can an infallible being be a creator? It would have to contain the correct answer to any possible question beforehand, containing an infinite amount of information. Such a being would be entirely uncreative and noninnovative since creativity involves the production of new information from a state where this information is not yet there. Evolution, as well as human thinking, are examples of processes that are creative in this sense, and they both involve chance and error.
An infallible god, on the other side, would not be able to create any new information. Everything must be there already. Such a god would not even have a history. A history requires change. The human being would not be created by it because all the knowledge involved would have to be there already. As it turns out, the idea of an omniscient creator is a logical contradiction. Either there is a creator, then it cannot be omniscient, or there is an omniscient being, then it cannot be a creator. It could develop into something, like a seed or egg that already contains the program for what it will become, or a computer that boots up, but it would not create. A creator, on the other hand, would have to be a system that starts from a state with less information and develops into a state with more information.
The universe we are observing is such a system. It contains processes that produce new information. And these processes involve, among other things, accidental events. In this sense, we could call the universe the creator.
Even if there was an intelligent designer, it would have to have a fallible, partially chance-based rationality. An omniscient system, on the other hand, would not be intelligent in any sense. It would be an algorithm of infinite size, but with no trace of intelligence or creativity. Intelligence is about generating knowledge, not applying it. Applying knowledge is something mechanical. An omniscient system could only apply knowledge.
So I think that the idea of an omniscient creator is based on a misunderstanding of what intelligence, creativity and rationality really are. A wrong model for human cognition is projected into the infinite and out pops the omniscient creator. Human cognition is able to invent all kinds of nonsense. This is a necessary consequence of its universality. An infallible system would be limited, an algorithm. The idea of the omniscient creator god, it turns out, is one of those unavoidable instances of nonsense.
(The picture is from https://commons.wikimedia.org/wiki/File:God-Architect.jpg)