Almost half of Americans believe that the entire universe was created within the past 10,000 years.
I am a centrist on creationism, as on most issues. I am with the 38% who believe that God has superintended evolution over millions of years. I think the "young earth" view is completely implausible.
So why do so many people believe in young earth creation? I believe it is because most people have no sense of history beyond their own grandparents, or perhaps their great-grandparents. Beyond that, all time seems equally distant. 1 thousand years, 10 thousand years, 10 million years, 10 billion years -- to a huge plurality of people, these are all just different ways of saying "a long time ago."
To be sure, there are some well-educated people who believe in young earth creationism. For them, their primary commitment is to the Bible; moreover, they are committed to a particular theory of Biblical interpretation. Young earth theories are a loyalty test to their more important intellectual commitment to their view of Scripture.
For the mass of people, the other 44.99 of the 45% of Americans who profess a young earth view, the important thing is that God is in charge. How many years God has been in charge is a quibble. What matters is that God has been in charge for all of the years that there have been. How many that is doesn't matter in any way that affects them.
When most people check the box on the poll marked "God created the world pretty much in its present form within the last 10,000 years" they don't really mean 10,000 years as opposed to 10 million or 10 billion. They mean "God created the world and I don't care what number you use."
Young earth creationism reflects innumeracy. But it reflects a deeper commitment to God's sovereignty.