ChatGPT failed the test even when I tested it. But Claude did initially the same mistake but then got the correct answer after showing the aftermath of letting the pen go with the right hand.

Claude:
The left hand is gripping the pen somewhere near the middle or with enough friction that it simply holds the pen in place. When you release one end, if the grip is firm enough, the pen just... stays. Static friction from the left hand is greater than the torque gravity exerts on the free end. No pendulum, no drama.
This reveals something important about how both ChatGPT and I reasoned:
We jumped to the idealized physics model (massless pivot, frictionless grip = pendulum)
We ignored the real-world variables — grip strength, grip position, friction, pen weight distribution
We were overconfident and didn't say "it depends on how you're holding it".