Fallibilism is the idea that we can never be 100% certain that we are right, and must therefore always be open to the possibility that we are wrong. This might seem a pessimistic notion, but it is not. Ironically, this apparent weakness is a strength; for admitting one’s mistakes is the first step to learning from them, and overcoming them, in science and society.
Fallibilism lies at the heart of the scientific enterprise. Even science’s most well-established findings—the "laws" of nature—are but hypotheses that have withstood scrutiny and testing thus far. The possibility that they may be wrong, or be superseded, is what spurs the generation of new alternative hypotheses, and the search for further evidence that enables us to choose between them. This is what scientific progress is made of. Science rightly champions winning ideas, ideas that have been tested and have passed, and dispenses with those that have been tested and have failed, or are too vague to be tested at all.
Fallibilism is also the guiding principle of free, open, liberal, secular societies. If the "laws" of nature can be wrong, then think how much more fallible are our social and political arrangements. Even our morals, for example, do not reflect some absolute truth—god-given or otherwise. They too are hypotheses—biological and cultural attempts to solve the problems of cooperation and conflict inherent in human social life. They are tentative, provisional, and capable of improvement; and they can be, and have been, improved upon. The awareness of this possibility—allied to the ambition to seize the opportunity it represents, and the scientific ability to do so—is precisely what has driven the tremendous social, moral, legal and political progress of the past few centuries.
Fallibilism—the notion that we may not be right—does not mean that we must be entirely wrong. So it is not a license to tear everything up and start again. We should respect tried and tested ideas and institutions, and recognize that our attempts to improve on them are equally fallible. Nor does fallibilism lead to "anything goes" relativism—the notion that there is no way to distinguish good ideas from bad. On the contrary, fallibilism tells us that our methods for distinguishing better ideas from worse work, and urges us to use them to quantify our uncertainty, and work to resolve it. Better still, to work together. Your opponent is no doubt mistaken, but in all likelihood so are you; so why not see what you can learn from each other, and collaborate to see further?
Anyone wishing to understand the world, or change it for the better, should embrace this fundamental truth.