Barbara Tuchman writes:
Wooden-headedness, the source of self-deception, is a factor that plays a remarkably large role in government. It consists of assessing a situation in terms of preconceived fixed notions while ignoring or rejecting any contrary signs. It is acting according to wish while not allowing oneself to be deflected by the facts.
I am trying to come up with examples that would support with Tuchman's quote.
To keep things as general and non-controversial as possible, I would argue that some of the basic differences between the Republican Party's values and the Democratic Party's values could be looked at as "wooden-headedness" (which seems to be another way of saying "hard-headed"). If you do not wish to dig into the political realm, however, I would encourage you to think of any personal examples of times you've experienced an argument with someone who saw things exactly the opposite as you did, and fought their side with as much passion.
I think teachers experience "wooden-headedness" every day. Most 9th grade English teachers (in NC at least) would agree that the End of Course test for 9th grade is a bit of a joke. The skills it covers should be considered low for a 9th grade level of comprehension. Most of us would also agree that reading-comprehension and writing skills are best developed by practicing reading and writing. Unfortunately, so much rides on the percentage of pass-rate on that test, that most 9th grade teachers forgo teaching full novels and writing full essays in order to spend more time practicing for those multiple-choice benchmarks and EOC. We would all agree that there is some "wooden-headedness" in the principals, school board, and legislators who seem to belive that this standardized test is the most important part of the 9th grade curriculum. Unfortunately, due to funding which affects the entire school, we will not risk the chance of lowering scores by making major changes in our classrooms. For that, perhaps many of us are "wooden-headed" as well.
I hope this personal example can help you generate some ideas of your own. Some other subjects to consider (outside of politics) that by nature seem to spark notions of "wooden-headedness" are religion vs. science, gay-rights, abortion, and global warming, to name just a few.