Whenever I'm processing a situation like Expert vs. Science, I try to bring a very specific lens into focus, and that lens is 'Centralization vs. De-centralization/Distribution.' That may sound confusing, and at first it might not lend itself to the subject matter, but I'll try to make my case in (a layman's employment of) anthropologic terms.
As humans we best operate in groups of 150-200 individuals. This has been demonstrated time and again using hundreds or thousands of different methods of inquiry. In such a group, you can only 'afford' to acquire/maintain one, or maybe at most TWO, high-skilled professionals of a given type (Doctor, Lawyer, etc..) in such a relatively small community.
If humans, hundreds or tens of thousands of years ago, didn't learn to TRUST their 'doctors' and 'lawyers' and other types of 'leader,' we'd have never made it where we did. We HAVE to trust our 'experts' to a certain degree, otherwise nobody would follow the 'doctor's advice and (assuming the doctor has a minimum degree of quality) more people would die than if people DID trust the doctor. So the survivors were the ones who were willing (if not eager) to defer their individual agency and ability to inquire over to the 'professionals' in certain situations. They learned to *selectively* CENTRALIZE their decision-making on Big Scary Issues because doing so provided rewards, generationally speaking, that outweighed the costs.
This mechanism, that the 'appeal to authority' system is built upon, is a fundamental component of ALL human sociology. I know this is a simplistic approach to the issue, but I'm convinced it's a valid (if not perfect) way to understanding why some people are inherently more 'okay' with surrendering their ability to reason on a given issue. Because, like Matt says, it IS scary thinking about things we legitimately *can't* UNDERSTAND. No human (I don't care if you're Joe on the street or Carl Sagan himself) has an innate ability to look up at the stars, contemplate the vastness of reality (as we understand it) and not feel overwhelmed/terrified. Some things are just too far beyond our monkey brains' ability to process, and on those things we're WAY more susceptible to the influence/opinion/leadership of supposed 'experts.'
And what's the most terrifying prospect in life? You guessed it: death. So religion answers questions like 'what's the meaning of life' and its children like 'what happens during/after death?' with various ideas that maybe don't make us feel a whole lot better about the prospect, but that ABSOLUTELY fit pattern recognition and 'make sense' to us sufficiently to make us think 'okay, the experts have probably got this one figured out better than I do, so I'll go with them on it.'
So science lets us do something VERY interesting to CENTRALIZED decision-making, whether it's in the form of Experts or anything else: it lets ANYONE employ an ultra-simple set of powerful tools to determine whether or not claims made by the Experts are legitimate. If such claims are disproven, the Experts lose their credibility. If such claims are not disproven, the Expert's standing remains strong (or potentially even improves). Theoretically, science could *also* let us almost completely DECENTRALIZE decision-making on difficult issues--at least it would allow CENTRALIZED decisions to be 'crowdsourced' rather than made by a small panel of exclusive 'Experts,' which is a step toward decentralization of authority (just like the USA's Representative Republican Form of Government decentralizes the decision of WHO gets to have supreme authority--the authority is still CENTRALIZED in an individual or body, but the community is able to employ DISTRIBUTED decision-making to determine who gets to wield that authority).
Bah, I rambled again. Almost hit 'delete' because of my thought sprawl, but decided to post it anyway.