Vonnegut's dystopian view of a society in which the government forces people to be "equal" is a rather disheartening one. In Bergeron's society, no one is too pretty, smart, strong or excellent in anything. As a result, supposedly, no one ever gets their feelings hurt, no one is offended, and happiness is supposed to abound--that is the purpose of equality, right? Happiness? Not ever feeling inadequate, confused or hurt? Handicaps keep anyone from excelling or inadvertantly hurting other people's feelings in this tale, and these handicaps are enforced by the government itself.
Does the government succeed in making everyone equal and happy? Look at Harrison's parents--his mother is constantly sad and crying, without ever knowing why. She feels bad for her husband, and confused all of the time. His father is always baffled, confused, alarmed and unhappy himself. He just can't pinpoint why. Harrison is miserable, and in prison for having the audacity to be excellent. People are always walking on eggshells, careful of what they do or say for fear of getting in trouble, or offending others.
Taking all of this into consideration, Vonnegut seems to be indicating that equality enforced by the government might be possible, but with great sacrifices and highly undesirable results. Government-enforced measures to "ensure" equality are, first of all, impossible, and secondly, devastating to happiness, freedom and agency. Everyone is NOT happy--they are confused and miserable; they don't know who they are; they can't own their own happiness. Everyone is mediocre and there is no joy. Even the ballerinas and musicians don't give joy through their performances--the only gleam of excitement, beauty, joy and happiness in the entire thing is Harrison's brief dance with his beautiful ballerina. Glampers, who shoots them both down, represents the government's interference in people's pursuit of happiness: it kills all hope, all possible chances of happiness and fulfillment.
I hope that those thoughts helped; good luck!