It's often used to find the root of a problem or set of values when the questioner doesn't know the issue with enough precision to fairly discuss it with the subject.

And most of the time the theoretical "goal" is to examine a belief or potentially invoke doubt on a belief previously considered solid rather than reach any conclusion.

Anecdotally I recently fell into this line of discussion with an anti-vaxer friend of mine. Instead of trying to persuade him he's wrong I asked questions about his beliefs and asked him to justify his decisions. Questions like "You were vaccinated, did that negatively impact you?" or "Do you worry about your children getting those sicknesses?"

Questions meant to clarify or examine, not persuade. In the end neither of us changed our positions on the topic, but if we're honest that was never on the table.

At least now I have a clearer understanding of his perspective and he was willing to share some of the more vulnerable details of his beliefs that he wouldn't have admitted had I come at him persuasively.

I do this in person and in online forums like this one. I'm not trying to guide someone to my own conclusion, and I might not have enough information to have an educated opinion, or I might be ambivalent about the subject. It takes the form of me asking for clarification in a non-antagonistic fashion.

I would say I most often use this strategy to force people to justify their own opinions to me when I have no opinion at all. I even do this to people I agree with.

Exactly. And this becomes very clear in the video. The interviewer harps on about the "reliability of faith" without really listening to what Antony is saying. Different people who are having different faiths but still believe in the same thing is only illogical if you wish to see it like that. All programs in your computer, for instance, can safely assume that memory does exist. There is no point for a program to find out whether something like memory is real. I am not talking about finding out whether space is left etc. I am merely saying that a piece of software does not need a science library to investigate the existence of memory. Sure, sometimes you don't receive something from memory when you need it, sometimes bad things happen when you work with the bits it gives you and so on. But questioning the existence of memory is besides the point.

Now lets imagine another program which also "believes" in the existance of memory The user uses this program to remove the other program. In other words, two programs who have the same "faith" kill each other. This is not a contradiction.

Someone should do the Socrates on him to elicit why "reliability" is something one has to discuss when it comes to faith. I am pretty sure his answers would also be contradictory within a short amount of time.

Yes, that's my point. It's the interviewer who has this idea that faith should be reliable and that's what I was questioning. Or did you mean the interviewer (Anthony with an h) ? I am a bit confused right now..

1) Person A: I hold a belief for which there is no proof or rational support. I just have faith in it.

2) Person B: I too hold such a set of beliefs. Mine are different than yours and they even compel me to kill you.

What interviewer meant is that this method of thinking arrives at vastly different, even conflicting views, hence it is inconsistent and unreliable.

It seems that it is a method for discussing ideas.

... when done on a level playing field. That's not what usually happens when people want to deal with "an opinionated colleague, manager or even a relative" (as the OP suggests).

I like the method because you can learn why people believe something along the way. Sometimes you might even change your own view based on their reasoning.

To discover what others think, know, or believe; not to change their mind.

Argument: the act or process of arguing, reasoning, or discussing.