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 whythreatens
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.