An two-step explanation for distrust of science: (1) journalists write up poor science or take out the evidence and information from a scientific study, then (2) people read that and criticize science for being unfounded, arbitrary, etc. Link. Some fun quotes:
Statistics are what causes the most fear for reporters, and so they are usually just edited out, with interesting consequences. Because science isn’t about something being true or not true: that’s a humanities graduate parody. It’s about the error bar, statistical significance, it’s about how reliable and valid the experiment was, it’s about coming to a verdict, about a hypothesis, on the back of lots of bits of evidence.
and
So how do the media work around their inability to deliver scientific evidence? They use authority figures, the very antithesis of what science is about, as if they were priests, or politicians, or parent figures. “Scientists today said … scientists revealed … scientists warned.” And if they want balance, you’ll get two scientists disagreeing, although with no explanation of why (an approach at its most dangerous with the myth that scientists were “divided” over the safety of MMR). One scientist will “reveal” something, and then another will “challenge” it. A bit like Jedi knights.
The danger of authority figure coverage, in the absence of real evidence, is that it leaves the field wide open for questionable authority figures to waltz in. Gillian McKeith, Andrew Wakefield, Kevin Warwick and the rest can all get a whole lot further, in an environment where their authority is taken
as read, because their reasoning and evidence is rarely publicly examined.
I think the deeper problem is that support for scientific findings is inevitably too complex for everyone to understand. Everyone hates statistics, so everyone has no choice
but to trust those that know do it.