It's only a toy example, and it already has a problem: people aren't very good at explaining their motivation. There doesn't have to be any logic to it, so you basically are in no position to question any preference by appealing to logic. People are also tempted to simply reply when asked, even if they don't know the answer. And your conclusion isn't fully justified either. Suppose the true, underlying reason for liking that team is

    coach == "my fav coach" || center_player == "my fav player" || won_last_match

and the team did in fact win the last match. Then the answer "because the coach is my favorite" is a fair answer, but changing the coach doesn't change the outcome.

This technique may very well set you on a path to misunderstanding when applied rigourously.

No, you misunderstand the goals and methodology. It might be better if you watch some full examples somewhere.

> people are also tempted to simply reply when asked, even if they don't know the answer

People are intentionally given as much time as possible and not pressured into answering. This is something they focus on consciously. Conversations are even ended with exchange of contact info in case they want to follow up.

The point is not to "win" but to get them to think about why they believe something and actually come to a conclusion (but not necessary right now.) It's acknowledged that this may even strengthen their original position, which is seen as a good thing. The point is not for the questioner to argue anything or come to any conclusion.

I'm not particularly well versed in SE, though I've watched many videos and listened to many podcasts. I feel like the example of a favorite sports team is ineffective because all practical conversations are around a belief that is substantive and meaningful to how one lives their life (with some detours to understand the nature of reality, such as the Tic Tac test).

So instead, maybe somebody says they don't trust vaccines because they know someone whose kid was diagnosed with autism after getting vaccinated. A potential follow-up question might be, "Do you know anyone who was diagnosed but who didn't get vaccinated?" Or a hypothetical, "What if you met someone who was diagnosed but who didn't get vaccinated? Would that change your belief?"

Getting them to work their own way through their beliefs - not necessarily to change said beliefs but to examine them - is the point. And given what I feel can be some REALLY far out beliefs than people have, I think it's normal to see SE practitioners sometimes lose their cool a bit or have their opinions/beliefs show.

>The technique is NOT to argue the truthfulness of a belief, but to focus on the reason for the belief.

That would be where good epistemology comes in. We're concerned with the quality of the knowledge (rather than its truthyness).