I think that it has to do with history. Generalissimo Chiang Kai-Chek's Kuomintang (Nationalists) and Mao Tse-Tung's Communists were bitter enemies, and fought for control of China for nearly 20 years before the issue was decided in 1949.
Chiang came close to destroying the Communists about 1936, but Mao (with Chou En Lai) saved the Communist Army through the brilliant retreat known to history as the "Long March."
The Kuomintang's monumental corruption and inefficiency were as much a threat to "free" China as were the Communitsts, so they were unable to "finish-off" the Communists.
The two sides fought each other as much as they did the invading Japanese in World War II.
Mao was very favorably disposed toward the United States, but partly because of Madame Chiang's charisma, (and because Chiang made encouraging noises about Democracy) the Americans threw in their lot with the Kuomintang.
Predictably, Chinese peasants saw the Communists as their advocates against the depradations of their landlords, who (predictably) were supported by Chiang's Kuomintang.
When the Japanese surrendered, the Russians occuppied Manchuria, and gave enormous amounts of weapons to the Communists.
The Americans continued to supply an increasingly corrupt Kuomintang regime.
Inevitably, the Communists gained control of China province-by-province. Finally, with US help, the Kuomintang evacuated their last foothold on the mainland, Canton, in 1949.
Chiang and his followers retreated to Formosa (Taiwan)and the small islands of Quemoy and Matsu. They continued to be the DE JURE Chinese Government until expelled by the United Nations about 1971. They styled themselves as the Republic of China.
The Authoritarian Chinese regime views Taiwan as an uncontrolled national territory, and will NEVER recognize the independence of another nation-state there. Taiwan continues to call itself "The Republic of China," and uses the 1912-1949 flag. (Which I think is a much prettier symbol of China than the one used by the Communists.)
The Chinese (on both sides) are a patient people. They always consider the "long view."They will wait several hundred years if necessary, but sooner or later, China will be ruled by one government.
What puzzles me is this, "Why is the US Government always kissing-up to the Authoritarian Regime?"