The premise of "Harrison Bergeron" is that everyone has been made equal. This is done by agents of the Handicapper General, who ensure that people wear artificial handicaps. These handicaps include mental handicaps for the smart, weights for the strong, and masks for the beautiful.
Early in the story, Hazel is described as having "a perfectly average intelligence." This means that she is, by our standards, extraordinarily dumb. Without a mental handicap, she still cannot remember why she is crying, even while the tears are still wet on her face. This lack of intelligence makes it hard to hold a conversation.
George, without his mental handicap radio, would be more intelligent. The device he is required to wear makes a dreadful noise (examples include a buzzer, breaking glass, and a car crash). This disrupts his thoughts on a regular basis, every twenty seconds or so, making it impossible for him to form a coherent train of thought.
Separately, both George and Hazel would have trouble carrying on a conversation. Together, they have no chance of more than a very basic conversation.