Well, first, you can't really believe the earth is 6000 years old and believe the science behind evolution. The two ideas are contradictory.
Bill Nye put it pretty well. The reason it's so important is that scientifically literate people are important to our nation's future. We're falling behind in math and science, and it's getting worse. America's status as a worldwide leader of science and innovation is at risk. We're a country that went from the Wright Brothers' first flight to landing on the moon in 66 years. Now we're sliding backwards. A growing number of people are rejecting enormous amounts of scientific evidence. Mostly out of spite, I think. Those heathen liberals believe in evolution, so it must be a lie. As Bill said, don't do that to your kids, because we need them.
There are any number of fields of science that one simply cannot succeed in while willfully rejecting so much evidence. And even in an unrelated field, the underlying mindset can seriously hamper your progress, because the ability to mentally suppress acknowledgment of evidence is not a good skill for a scientist.
Perhaps worst of all, in my opinion, is just that creationism is an idea that assists in the suppression of curiosity. It's not everyone, it's not all the time, but I think the push is there. When one blindly accepts a religious text as having all the answers about the universe, there's no need to ask more questions about it. Even if you're not a scientist, someone taking the biblical story of creation literally already "knows" how the universe was created, so why would they become curious about it? And to me, curiosity is God's true gift to mankind, along with the intelligence to act on it. Curiosity got us out of the cave, over the mountain, across the ocean, and into the skies. And to space and back. It's built in. Genetic. Every child goes through that phase. The "why?" phase. "Because God did it" is detrimental to the why. It hampers true understanding, and I don't that's what God would want for us.
And, to be perfectly clear, this isn't everyone. It's not all Christians, nor all people of any other religion. It's not even a majority, I don't think. There are innumerable Christians of any denomination who understand, explore, and advance any field of science. Or even just get curious about them and learn. But I don't think a 6000 year old earth lets you do that. I don't think an Einstein or Hawking can exist within that mindset.