Taiwan was formed after a civil war. They believe themselves to be independent. Enough to break off from China.
Stop embarrassing your lack of Chinese history.
The KMT fled to Taiwan after loosing the Chinese Civil War. At the time of KMT's defeat, Taipei became the de-facto capital, of the officially recognized government of
CHINA,
not an independent Taiwan. The government in Beijing was later recognized, as the official government of China, once the rest of the World realized that the cause of KMT was over. Throughout the rest of the 20th century, the KMT still maintained that they were the rightful government of
CHINA.
The pipedreams, of an independent Taiwan, was created and primarily fueled, by US imperial policy, in the region to contain China. Nothing more, nothing less.