If you ask someone "why?" enough about a subject you don't agree on, eventually both of you will come to a conclusion
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
We use this at work a lot when there's been some kind of failure. The idea is to try and get to the real root cause of an issue, not just the immediate cause. Like maybe an engine failed because a valve didn't open - you could correct that by replacing the valve, but why didn't the valve open? Maybe it was stuck and the initial force to open it was more than the actuator could handle. Okay, so maybe we could lubricate it somehow, but why was it stuck. Maybe the supplier changed their cleaning method and switched to a new chemical. Why did they do that? Oh, because it was cheaper. That's the real root cause: the supplier tried to cut costs by switching to an inferior cleaning chemical. Time to work with them to fix that. All of the other fixes would have only helped that one valve on that one engine - this one fixes all of them.