Jar, I'm simply choosing your post to respond to, because it works. This is more of my general input to the thread, for whatever it's worth.
We see this all the time with Young Earth Creationists and Biblical Literalists. They simply refuse to acknowledge reality of either the world they live in or the book they claim to follow.
They choose to believe that they are right even though all of the evidence shows that they are wrong scientifically and theologically.
Kenneth Miller, whom I have a lot of respect for, met Ken Ham, who is defined by your quote here. Amazingly, Kenneth Miller walked away saying he understood how Ken Ham could believe what he believes. I spent days thinking about this.
Ken Ham surely fits your definition. It would seem that he "chooses to believe he is right even though all of the evidence shows that he is wrong scientifically and theologically."
I don't think it's that simple. "All of the evidence" may be subject to some wide interpretation. Whatever Ken Ham's reasons are for believing that the Bible is God's literal Word on science and everything else, he has reasons for believing that. You can reject that as evidence, but to him his reasons are real evidence. Perhaps it's experiences in his life or just the word of his parents.
My point is that he is not purposely believing what he knows to be false. He is choosing his evidence, as terrible as it might be, over all other evidence that he sees, choosing to believe that the opposing evidence is instigated by satan in some way he cannot understand.
I think he's a fool. However...
There is an arrogance (overconfidence may be a better word) among "intellectuals" that I feel all the time. I remember a discussion on here about whether a good God could exist in a world full of evil. One person had nailed the whole discussion down to three possibilities. When I suggested that there was a fourth possibility, which is that there's things we don't understand about evil and suffering, and we're missing something in our analysis, he couldn't even process the thought. I think that person is at least as great a fool as Ken Ham.
Personally, I think the reasoning of Ken Ham (and many others) goes something like this: "I was raised to believe that God saves people through Jesus Christ. As I grew up, I saw this belief work very often. I see belief in the Bible as a positive influence and even as a supernatural influence in the world. Therefore, what the Bible says on science is to be trusted, and scientists are not to be trusted. They're probably tricking me."
As I said, I find lots of problems with that reasoning. However, I don't believe it's in any way true that Ken Ham and those with him are simply choosing to believe falsehood.