Why is the government searching for Harrison Bergeron?

In “Harrison Bergeron,” Harrison has been locked up because  “he is a genius and an athlete, is under-handicapped, and should be regarded as extremely dangerous.” He has escaped from jail and is on the loose, and they are frantically trying to find him.  In this society, everyone was expected to be the same.  In other words, no one should be smarter, or stronger, or different from everyone else.  If a person danced too well, for example, he or she would receive a “handicap” to make his or her dancing worse.  “They were burdened with sashweights and bags of birdshot…”  Harrison’s father is forced to wear a device that makes loud noises every time he thinks more than he should. 

When Harrison bursts into the television studio, he takes off all his handicaps to reveal “a man that would have awed Thor, the god of thunder.  He removes the handicaps from the ballerina, and she is “blindingly beautiful.”   The handicaps they have been forced to endure are because the society does not want anyone to “feel bad.”  Harrison and the ballerina have a moment of blissful freedom before he is shot as an example to others who might want to be different.

Why is the government searching for Harrison in "Harrison Bergeron"?

There are four reasons the government is searching for Harrison Bergeron. The most immediate reason the government is looking for Harrison is that he broke out of jail. The second reason is that they suspected him of planning to overthrow the government. 

The next reasons the government is looking for him are specific to the future society Vonnegut evokes. The third reason is that Harrison is "under-handicapped." Under this future American government, people whose abilities or gifts raise them above average have to be handicapped. He isn't handicapped enough. And that leads to the final reason they want Harrison: he is an active, living, and vividly dramatic challenge to the government's conceptual and ethical foundation. Just by living and being strong, smart, and handsome, Harrison threatens them.

Why is the government searching for Harrison in "Harrison Bergeron"?

Harrison Bergeron, the fourteen-year-old son of George and Hazel Bergeron, had been arrested in April 2081 and put in jail. He was suspected of trying to overthrow the government, although how he would have done so or what he actually tried to do is not overtly described in the story. As George and Hazel are watching TV, they hear an emergency announcement stating that Harrison has escaped from jail, and his picture is flashed on the screen. Soon Harrison himself appears live on TV. He has torn a door off its hinges and proclaims himself Emperor. He then begins to remove all his handicaps--scrap-iron, headphones, wavy-lensed spectacles, and red rubber ball nose. He then chooses a ballerina for his Empress and commands the orchestra to play beautiful dance music. As he dances with his Empress, allowing people to "watch what [he] can become," Diana Moon Glampers, the Handicapper General, appears in the studio and executes him and the ballerina on live TV.

The government is looking for Harrison because he has escaped from jail and threatens to overthrow the government by showing everyone what human beings are capable of when they allow themselves to embrace their strengths rather than squelch them for the sake of equality.