For several decades, there has been an extensive and organized campaign intended to generate distrust in science, funded by those whose interests and ideologies are threatened by the findings of modern science. In response, scientists have tended to stress the success of science. After all, scientists have been right about most things.
Stressing successes isn't wrong, but for many people it's not persuasive. An alternative answer to the question "Why trust science?" is that scientists use the so-called scientific method. If you've got a high school science textbook lying around, you'll probably find that answer in it. But what is typically thought to be the scientific method — develop a hypothesis (假设), then design an experiment to test it — isn't what scientists actually do. Science is dynamic: new methods get invented; old ones get abandoned; and sometimes, scientists can be found doing many different things.
If there is no dependable scientific method, then what is the reason for trust in science? The answer is how those claims are evaluated. The common element in modern science, regardless of the specific field or the particular methods being used, is the strict scrutiny (审查) of claims. It's this tough, sustained process that works to make sure faulty claims are rejected. A scientific claim is never accepted as true until it has gone through a lengthy "peer review" because the reviewers are experts in the same field who have both the right and the obligation to find faults.
A key aspect of scientific judgment is that it is done collectively. No claim gets accepted until it has been vetted by dozens, if not hundreds, of heads. In areas that have been contested, like climate science and vaccine safety, it's thousands. This is why we are generally justified in not worrying too much if a single scientist, even a very famous one, disagrees with the claim. And this is why diversity in science — the more people looking at a claim from different angles — is important.
Does this process ever go wrong? Of course. Scientists are humans. There is always the possibility of revising a claim on the basis of new evidence. Some people argue that we should not trust science because scientists are "always changing their minds". While examples of truly settled science being overturned are far fewer than is sometimes claimed, they do exist. But the beauty of this scientific process is that it explains what might otherwise appear contradictory: that science produces both novelty and stability. Scientists do change their minds in the face of new evidence, but this is a strength of science, not a weakness.