The key is in the title: asking people HOW their position works, helps them realize that there may be gaps in this understanding and makes them more likely to moderate their views. Asking for a list of reasons WHY does not, as some people may have unjustified confidence in their understanding. So the next time you are at the bargaining table, or the kitchen table, ask "how would that work?', "how would that impact...?" or "explain what you mean by...?"
This is one of the simplest and most powerful methods of persuasion. It’s easier to get people to persuade themselves than for you to persuade people.