I don't mean to personalize this to you, but your story kinda illustrates one of the problems. There's so much ego and self-worth tied up in both sides of this style of "interview". Both sides have this overwhelming need to show how smart they are.

It's understandable in some ways. It's part of what attracts people to the field, showing off intelligence. I'm guilty of it myself.

But it makes the "interview" process have an adversarial nature most of the time. That's not helpful to the actual goal of hiring people who will make your team successful.

One thing that might work along these lines- Bring in a hard problem that the interviewer doesn't know how to solve and spend some time trying to solve it with the candidate. As a team, discussing different options and problems with those options. You know, like people do in actual work situations...