Reason isn't the final arbiter

This entry below was a reponse to the following question: Certain hadiths especially regarding women do not make sense. These are not correct according to the dictates of reason and common sense.

How I have learnt to understand issues has a lot to do with what I have come to understand of "reason" itself: Once you get acculturated into historical debates on science, mathematics and theology (the crisis in the foundations of mathematics is an important episode) you realize that no idea, religion, or school of thought turns out to be water tight when it connects with "reason". There are always statements, ideas around the edges which reason has to overlook-even for hard sciences and mathematics, which were long considered to be outcome of purely rational activity. Otherwise much of what we have achieved in terms of scientific and intellectual progress will be undermined. A lesson one learns is that if one can't square everything with reason, one doesn't throw the idea out of the window. Rather one looks for something deeper. For example the contradictions in mathematics in the early part of 20th century led to our deeper understanding of numbers (that they are intuitive, and not reducible to logic), and led to far more modest view of our understanding of mathematical truths: the faith in the necessity of mathematics was forsaken, but it lead to new lines of mathematical growth, more open-ended. When the positivists (followed by sociologists/historians) began to analyze science they ended up radically changing the very conception of science: They (historians) showed that: (1) There is no way to tell if science is progressing; (2) Showing a superiority of a theory over another is not a simple matter; (3) Our observations are theory-laden i.e. presuppose the very theory being tested, and thus there are no independent observations; (5) Much of science is based on aesthetic considerations such as that of symmetry which are intuitive and not rational. 
I think there are various competing conceptions of reason, all arbitrary to a certain extent. Perhaps there is something abiding at the core, but that is difficult to articulate. And these conceptions are entire cultures and world-views which become one's rational cognitive structure though which one processes beliefs, but are seldom themselves scrutinized. This cognitive disposition is determined/altered by one's own psychological inclinations, culture, background and importantly one's reading of the history of reason itself (How one reacts to Zeno's paradoxes; say, are they really that important?). This is basically our readiness to believe a certain kind of thing, even as it violates strictures of reason. Who would have believed that light is particle or wave depending on how the observer expects it to behave.
Therefore, I think to overlook somewhat, and not always insist on the logical consequences, is still an intellectually responsible position since reason itself is not immune to absurdities and one just can't expect a true theory/faith/religion to entirely correspond with it. (Example: Zeno's paradoxes, showing that motion is impossible, are as instructive as they are shocking: innocuous assumptions leading to insurmountable contradictions).
In fact, there is no such thing as reason standing apart from every idea and theory and judging it-reason itself is affected by and involved in those ideas. It's an admixture of reason/intuition/insight which coalesce to bring one to see things as we do. A number of people converted to Islam when they saw the face of the Prophet Muhammad (saw)-they said it couldn’t be a face of a liar. Or, what I once heard: "A believer's best argument is his face". Will we discount this intuition as inferior to reason. I know I am not really answering your argument, but I just wanted to say that there are other faculties than reason which are also important. Furthermore, I think your belief lies is some place other than your reason, and you use the latter just to give it retroactive intellectual respectability and, to take  comfort in the thought that it makes sense-it would make us mighty uncomfortable if it didn't but that would not make us give up a belief. It isn't that easy. Try this thought experiment: "Killing children is wrong" just can't be shown to be true through reason alone, yet you are so hard-wired to believe it that you will not accept any ideology/religion which holds to the contrary.