Many hold strong beliefs and opinions, however not many know the roots of their belief. If a person agrees to explore it, both of you will learn something new and fascinating. The problem is finding someone who wants to think and ask the questions. This goes for both. Many want to “convince” someone, but how much do you truly know about the thing you’re trying to prove?
This also comes back to the “why?” game so many kids play. Parents get annoyed by it, but are they really annoyed at the game or their lack of knowledge depth? Play the game, find out how deep you lake of knowledge goes
This process is generally referred to as The Socratic Method. As you said, the devil is in first convincing both parties within a debate that they should be searching for shared understanding through the process of attacking and defending ideas, not attacking and defending each other.