Angular Momentum on a Rotating Stool

What happens when you change your moment of inertia while rotating? Here I sit on a rotating stool while holding two 1.00 kg masses, one in each hand.

Moving the masses towards or away from my center of mass affects my moment of inertia. This has an effect on my moment of inertia.

Since there is no net external force or external torque on me, angular momentum is conserved. This means that as I increase my moment of inertia, my angular speed drops.

[cmclean]

Where can I purchase a rotating stool like this?

[TheAnimammal]

This demonstrates conservation of angular energy and contradicts conservation of angular momentum because in reality, angular momentum is not conserved. Humanity has been making a stupid mistake for three hundred years because we are so easily convinced by things "spinning faster".