I've been troubled by this forever too. I recently came upon a meme that sums it up for me, at least at this moment. It is this: the anger of some on the right can be attributed to a determination to "get back at those damn smart kids". They are tired of being pushed around, they hate that stupid logic stuff, and its time to put those smart kids in their place.
As a result, it's unfair for those smart kids to keep winning the argument, or proving that the right is illogical, or bringing up complicated issues that are hard to accomodate in a simple worldview, so it's the right's turn to be in charge.
For me, this explains why the wall goes up when you try to argue with some of these people. You've identified yourself, and so you need to be put in your place. Or, if you persist in discussing issues, your logic and evidence is somehow "unfair" or inappropriate.
Of course, not everybody on the right has this attitude, but it's major feature of the movement in general.