Why is Harrison Bergeron such a threat to society?

A good question. First, let me refer you to the earlier answer by ask966. It makes good points about why Harrison Bergeron threatens his society so intensely.

I would add several other points, though. The first is a variation on the points ask966 made. Harrison is not just above the enforced equality that defines his society. He is in many ways impervious to the restrictions they society places on him. He is weighed down and disrupted, and he still rises above the restrictions, limits, and other handicaps. He literally rises above the handicapped state in the final dance scene.

Second, by demonstrating that he is not equal, he provides a living example of his society's limits. He's like an infection. Everyone who sees him dance will know in a vivid, dramatic, and beautiful fashion that people are not equal.

Because he is heroic, he will inspire others to rebel. He has died, yes, but who knows how many people will be inspired by the memory of his actions.

The memory will also show that the society was unable to anticipate his actions and capabilities. This shows there are limits to the government's power, something that should also nudge people to rebel.