The government, and the citizens, of Taiwan, do not recognize themselves as part of China, hence the constant threat of invasion by China and their annoyance at the US for sending Taiwan arms and defense weapons.
You may want to reeducate yourself on that. The government officially considers itself Republic of China, just not PRC China. The ROC still claims all of mainland China (including modern day Mongolia) but only administers the province of Taiwan. Some citizens may no longer consider themselves Chinese but the government in Taiwan hasn't declared the island as its own national entity. The official political position on both sides of the strait is that the civil war for the entirety of China is still ongoing but a frozen conflict. In fact, the ROC government continued to appoint (largely symbolic) governors to all the Chinese provinces up until the 90s and the position of the governor of Fujian Province exists to this day due to their presence in Kinmen and Matsu.
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