https://amgreatness.com/2018/08/16/protecting-taiwan-from-chinese
The Chinese want to regain Taiwan as much as Abraham Lincoln desired to keep the southern states in the Union. Since the day that Taiwan became home of Chiang Kai-shek and his displaced Chinese Nationalist forces, the United States has vowed to uphold Taiwan’s place as an independent country. China views Taiwan as a breakaway province. The United States sees Taiwan as a democracy besieged by a larger, bullying neighbor. Taiwan simply wants to be free and sovereign.
A Complex Relationship: China, Taiwan, and the United States
For its part, the United States strives to maintain a posture of strategic ambiguity. At first, the United States unequivocally stood behind Taiwan as a counterweight to Red China in the Cold War. During the Nixon Administration, however, U.S. policy toward China fundamentally changed. Nixon went to Mao and the two leaders opened up their countries to each other.
Later, as part of the Carter Administration’s diplomatic efforts with China, the United States no longer recognized its long-time ally of Taiwan as the legitimate government of China.Until then, Washington had only recognized Taiwan’s government as the government of China. But under Carter, Washington conceded the “one China, two systems” model that there is only one Chinese government—and that government is in Beijing, not Taipei.