Reason is a limited process because it arises from consciousness, which observes the universe via filters. The mind has physiological filters (ex, wavelengths of light you can perceive, frequencies of sound you are limited to), chemical filters (the specific biochemistry of your brain, your mood and emotion, etc), and mental filters (pre-existing ideas and biases, fidelity of your metal models and assumptions, simple lack of knowledge). These are all best understood of as filters between you and the “objective” truth of reality. The universe as you observe it and understand it is vastly more complex than you can understand. The process of reason happens only with information you can process at the end of that chain of filters, so you are always operating on an insufficient dataset.
The brain is actually evolved to extrapolate and infer information based on filtered input. The brain often fills in the gaps and makes us see what we expect to see rather than what is actually there. Simple examples are optical illusions and the way the brain can still make sense of the following sentence:
Arinocdcg to rencet rseaerch, the hmuan brian is plrectfey albe to raed colmpex pasasges of txet caiinontng wdors in whcih the lrettes hvae been jmblued, pvioedrd the frsit and lsat leetrts rmeian in teihr crcerot piiotsons.
As a result, there are not only filters on what we perceive but also active transformations of imagination and extrapolation going on that actively modify what we perceive. These filters and transformations all happen “upstream” from the rational process and therefore reason can never operate on an untainted, objective reality. Despite the filters and transformations, the mind does a pretty good job, especially in the context of human interactions on the planet earth (which is what our minds and their filters and transformations are optimized for, after all). However, the farther up the metaphysica ladder we go, the more we deviate from that optimal scenario for which we are evolved (or created, or created to have evolved, or whatever. I’ve not said anything to this point that most atheists and theists need disagree on).
A good analogy is that Newton’s mechanics were a fantastic model for classical mechanics, but do not suffice for clock timing of GPS satellites in earth orbit. This is because Newton did not have the tools available to be aware of general relativity. Yes, we did eventually figure it out, but Newton could not have ever done so (for one thing, his civilization lacked the mathematical and scientific expertise to formulate the experiments that created the questions that Einstein eventually answered).
Godel’s theorem makes this more rigorous by demonstrating that there will always be statements that can neither be proved nor disproved by reason. In other words, as Douglas Hoftstadter put it, Godel proved that provability is a weaker notion than truth, no matter what axiom system is involved. That applies for math and it applies to philosophy, it applies to physics and it applies to the theism/atheism debate.
Related – more detailed explanation of Godel’s Theorem and implications on reason.