One man's garbage is another man's treasure - and one man's lie is another man's truth. How can you bring someone around to your viewpoint? Maybe you shouldn't try unless you are also willing to change your stance. It is often said that people believe what they want to believe, regardless of the facts, so that arguments focusing on data may be less fruitful (for both parties) than other approaches. That's not to say you should debate with lies, of course. Instead, a friendly discussion of a fictional situation may allow for a less confrontational conversation. The science-fiction realm of Star Trek, for example, explores real-life scientific, social, ethical, religious, medical, and environmental issues in the context of fictional worlds - often with fictional races - which makes an analysis of the issues less personal between two parties by bringing in a fictional third party.
At the Public Library of Science (PLOS), microbiologist Maggie Fink and biochemist Dr. Shahir Rizk discuss the issue of combatting disinformation in a friendly, humble manner using "story plots", much like a Star Trek episode, rather than "data plots" that scientists are trained upon. We encourage you to read their thoughtful post which also touches on their conversations with flat-Earthers.