Modern man is convinced that evidence and logic are not only the best, but the only valid sources of truth; and that imagination or direct-knowing (accessed by intuition) is subjective, make-believe, open to infinite error; yet evidence and logic are always inadequate.
Evidence is useless - and indeed is not evidence - without a metaphysical system that defines what is evidence and how to interpret it.
The invalidity of logic is simply that it is a model - a grossly simplified version of reality. This is what makes it potentially useful, and also what makes it wrong.
The problems with logic are (at least) two-fold - first that the correctness of logic is unsure. The history of philosophical logic is one in which there are discoveries and refutations - for example, in relatively recent times by Frege and Godel; so that at any particular time and place we cannot be sure that there is not some error in our understanding of logic.
Plus: The potential for error is multiplied (exponentially) by each step in logical reasoning - so complexity of argument is less sure than simplicity.
Secondly - logic is an abstraction which must be applied, must be 'mapped-onto' real life - and this is where things most commonly go wrong.
The problem can best be illustrated by mathematics, which according to some theorists is ultimately identical with logic. To apply mathematics to Life, we need to assign numbers to the entities and process of life - and it is in assigning abstract numbers to real things that things go wrong. Much the same applies to logical categories.
One of the recurrent problems of Christianity (and many other religions) - which goes back a very long way - is the technical, mechanical use of evidence and logic to manufacture specific desired conclusions, to 'settle' questions. And then to rely on these evidence-logic-manufactured 'answers' to the exclusion of the discernment of the heart.
Something similar happens in science. Really creative science is a matter primarily of imagination - but imagination will not come when called, and will not do what it is asked when it is asked - so scientists are tempted to grind-out conclusions with evidence and logic, despite the lack of imaginative validation.
I have done this myself, many times, leading to contrived interpretations and conclusions that never stand-up to sustained reflection; and always regretted my impatience.
What is required is patient brooding, waiting upon the right answer to come in its own time and with its validating, certainty of evaluation of the heart.
I shall have more to say on this theme.