It all comes down to three problems, in what I believe is the order of prominence:
1. The way science is taught- Due to pressure to pass tests, children are taught to memorize facts about science and not taught how to critically think through the scientific process. The latter takes much more time, effort, and creativity on both teachers' and students' parts. As such we end up with a culture that treats science not as a tool, but as an approved collection of facts to know are True. If the gatekeepers of science say eggs are bad for you, then eggs are bad for you. If they say eggs are good, then the typical person doesn't reason through the explanation for why researchers have changed their minds, they express frustration that the researchers "can't make up their minds".
2. The way science is reported- Most newspapers do a poor job of reporting science. As others have said, headlines are sensationalized to move print. But another problem is that content may be simplified in order to not take up too much page real estate.
3. The way scientists represent themselves- I have a good friend who is endlessly frustrated by creationism. One time he told me that his biggest frustration was that every time he saw an evolution versus creationism argument on FOX News, the creationism side was represented by some handsome young man with a confident but non-threatening smile and perfectly styled hair, while the evolution side was always represented by some dowdy researcher who looks uncomfortable and can't articulate their point clearly within the framework of a 2-minute news interview segment. Or they look like Christopher Hitchens, i.e. they rolled out of bed, slammed a couple shots of vodka, and then showed up with no intention other than snidely insulting anyone who doesn't accept their position on faith. Shallow though it may be, image is part of presentation.
And my experience in academia is that this extends beyond evolution debates. Many academics enjoy being deliberately obtuse. I couldn't tell you how many papers I've read where Latin phrases get dropped in for no communicative purpose other than showing that the researcher knows Latin, or where language is needlessly complex, or where articles are laid out in a manner that makes it impossible to read their arguments without flipping back and forth across several pages in order to remember what the terms the author invented mean. Hell, I recall the GRE exam gives bonus points on its writing exam for crap like this, with a example essay talking about "a Sargasso sea of ideas" getting its top grade, despite the fact that such language doesn't make much sense to anyone who is unfamiliar with that particular region. When I hear professors talk about writers who distill research for casual audiences, while the words "dumb down" don't get said overtly, there is often a strong sense that such writing is beneath a real scientist.
But the biggest example of the way academia insulates itself from the outside is access to academic journals themselves. The whole process of science is built on the ability of the public to scrutinize and replicate experiments, but often access to scientific journals is quite expensive for people not in a university. How can we expect journalists to get our research right if we demand they subscribe to J-STOR just to read about it?