When you say "science", you need to distinguish between science as philosophy vs. science as an institution. Science as philosophy is a way of thinking - an attempt to understand knowledge and reality. The science as an institution on the other hand has all the imperfections as any other institution, since the people in charge are driven by self interest and not just the search for the truth. So, when you say the people distrust science, it seems bizarre that they doubt science as philosophy, while in fact they doubt the institution. It's perfectly fine to mistrust the institution. If you want to consider a few failures, just in the recent years, I have some for you:

- Hungarian-born biochemist Katalin Karikó, who developed the key mRNA modification that enabled effective COVID-19 vaccines, was repeatedly denied grants and demoted during her career. She and her collaborator, Drew Weissman, struggled for years to gain recognition and funding for their work [1]

- On the other hand, the Wuhan Institute of Virology had no trouble getting grants from NIH [2]

- Surgeon General Jerome Adams was saying that masks are not effective against Covid [3]

- Social distancing was of supreme importance, until it turned out that it's fine not to distance if it's for a good cause [4]

[1] https://www.statnews.com/2022/02/01/kariko-problem-lessons-f...

[2] https://www.bmj.com/content/382/bmj.p1701

[3] https://www.npr.org/sections/health-shots/2020/07/01/8862991...

[4] https://www.politico.com/news/magazine/2020/06/04/public-hea...