What is behind the creationist rejection of natural history?
We can only answer this question by looking at its history and context. I want to commend @TedDavis for doing this, but I think that something is missing that is basic to the answer.
Conservative Christians about 100+ years ago saw scientific thinking as a threat to the Bible. A prime example of this was evolution which put in doubt the accuracy of Genesis 1. Instead of trying to find a way to explain this and reconcile these narratives, conservatives sought to strengthen the Bible’s claim to truth, esp. Genesis, by saying that Moses wrote Genesis under the direct inspiration of God.
They said that the Bible was God’s Word, despite the fact that John 1:1 says Jesus Christ is God’s Word. By making the Bible God" s Absolute Word, the Fundamentalists made the Bible God’s Mythos, the Word that must be accepted based on authority. On the other hand God’s Word (Logos), is believed, because there is evidence that it is true.
Jesus is not the Messiah, because He claimed to be or the Bible says He was. Jesus is the Messiah, because He did what the Messiah was supposed to do. (Clearly most Jews disagreed.)
The Fundamentalists by making the Bible the Word/Mythos gave it authority, but also made it an idol or false god. They also made their faith into a sect which is cut off from the rest of Christianity and Western Civilization, including science.
Then Bible is a good book, but it is not the Word of God, Jesus is, Science is good, but science is not the Word of God. Jesus is.
Darwinian evolution has a problem in that Natural Selection purportedly works by chance and conflict rather than the Logos. Also evolution is not as simple as genetic change. However the Darwinian process was basically correct. But because Creationists have a non-scientific critique of evolution, they are unable to debate and possibly correct the real scientific issues.
The Big Bang Theory actually supports Genesis 1, but because it is scientific and YEC has already denied related science because of its 6 Day view, it must reject the BBT also. Bad theory has put it into a box that it cannot escape without basic changes.
The Big Bang theory on the other hand causes problems for the non-believer. It says that the universe emerged from nothing, Before the Big Bang theory the was no proof that the universe has a Beginning and thus no scientific verification that it has a Creator. Now there is but a YEC cannot use this evidence because YEC rejects this science.
On the other hand non-believers like Dawkins seek to deny the BBT because they say that the universe did not have a Beginning, that time and space, matter and energy were created out of nothing. Thus non-believers are refusing to accept proven science because it indicates the strong possibility of a Creator.