Deng Xiaoping was concerned about the growth of this movement because he did not want to see Communist Party control disappear in China the way that it was disappearing in the Soviet Union.
Beginning in the late '70s, the Chinese Communist Party had begun to try to implement economic reforms. These are the reforms that helped to make China what it is today. But the Party was afraid that things could get out of control as they had in the USSR under Mikhail Gorbachev. Seeing what was happening in the USSR, Deng felt that the democracy movement was a major threat to the Communist Party and, thereby, to stability in China.
It is for this reason that he suppressed the movement.