they told him it was an IQ test but it was actually a psychological profile to diagnose his anger issues

For the same reason why he brought up his iq tests in the first place.

Because he self-identifies with some definition of iq.

Not at all. The authority figure simply could not live in a world where the question was wrong. A better response, in his role as a school teacher, would have been to tackle the question in depth as a class or otherwise show me how I was mistaken. But given as I was immediately dismissed I’ll never know for sure.