When Pope John Paul II published his encyclical Fides et Ratio (Faith and Reason), I was somewhat astonished. I thought it was obvious that truths known by faith and truths known by reason could not contradict each other. Of course, one has to be certain they are using words the same way; for example, when we say someone is a "big man" we may mean he is physically large, or that he is magnanimous, or that he is important. We love apparent paradoxes caused by the elasticity of language: "Napoleon was a small man, but he was also a very big man."
Unfortunately, the problem of language seems to extend to the very heart of the perceived conflict between faith and reason. Specifically, I recall a conversation I had with a woman on a train back in the late 1990's. The topic of faith came up -- I don't recall how -- and she asked how I could account for Muslims, Hindus, etc., all of whom appear to have just as strong a faith in contradictory ideas.
My response was that faith has to do with its subject matter; it is not merely a feeling, any more than guilt is just a feeling. Someone may feel guilty for something that no reasonable person could blame them for, such as being the only survivor of a crash that takes the lives of friends or family. Likewise, some people can commit the most atrocious crimes without feeling the slightest twinge of guilt; the guilt is there, but it is not experienced as a feeling.
For another example, take health. One person may be perfectly healthy in every important way but feel terrible due to something superficial; another person may feel just fine, but have an undetected cancer.
The conversation ended with the woman saying she had never thought of it that way, and that she would give it some more thought. In retrospect, I think she was far more representative of the general public than I realized: most people probably share her confusion between faith as a feeling and faith as way of knowing. In fact, I suspect that many people have a similar misconception about reason and confuse their emotional reactions to an exercise in reason.