Earlier quoted context omitted.
Let's not forget though that a great deal of "science" is in fact trash[1]. The problem isn't really people being anti-science or pro-science. The problem is science being done poorly, whether by scientists in the credentialed sense, or amateurs. There is no pat "trust science more" or "trust amateurs less" answer here. The actual answer is that if you want to understand research, you need to actually understand math…
I think there's two extremes here. One is the issue covered well above. There is a great deal of junk science that gets published. That is a problem and it does erode trust. But in some ways it's also how the sausage gets made, there's going to be room for things to get published they later gets refuted. People rightly so have distrust for results coming out in fields they don't have good knowledge in. Without becomi…
Put simply, science is advertised as self-correcting but in reality it's not. Representative experience documented here: http://crystalprisonzone.blogspot.com/2021/01/i-tried-to-rep...
So, the reasons people learn a generalized distrust of science are that often the sausage doesn't get made. Bad science is published, applauded, cited, breathlessly covered in the media and may even be replicated, yet the first time outsiders to the field actually read the paper they realize it's nonsensical. But then they realize nobody cares because careers were made through this stuff, so why would anyone inside the field want to unmake them?
The degrading trust doesn't come from bad results per se, but rather the frequent lack of any followup combined with the lack of any institutional mechanisms to detect these problems in the first place beyond peer review, which is presented as a gold standard but is in no way adequate as such.
For example, consider how programmers use peer review. We use it, and we use lots of other tools too because peer review is hardly enough on its own to ensure quality. Now imagine you stumbled into a software company that held a cast-iron policy that because patches get reviewed by coworkers you simply don't need a test suite, nor manual testing, nor a bug tracker, code comments, security processes, strong typing, etc. And their promotion process is simply to make a ranking of developers by commit count and promote the top 10% every quarter, and fire the bottom 10%. Moreover they thought you were nuts for suggesting that there was any problem with this. You'd probably want to get out of there pretty fast, but, that's pretty much how (academic) science operates. So of course this degrades trust.