Taiwan was returned to the Republic of China (ROC), ruled by the nationalist KMT, after the defeat of Imperial Japan, which had occupied it. The KMT forces lost the civil war on the mainland against the communists and fled to Taiwan, claiming to be the true government of China. The ROC was a military dictatorship until the late 80s and responsible for the White Terror. At first, the communist People's Liberation Army (PLA) couldn't follow and invade Taiwan because they lacked a navy, and soon after, the ROC got US protection (Taiwan was in important US military base during the Korean war).

In the 70s, Nixon recognized the People's Republic of China (PRC) in Beijing as the legitimate government of China, and un-recognized Taipei. He also signed an agreement with the PRC stating that there is one China, and that Taiwan is part of China. White House spokespeople reaffirm this regularly when asked. They never actually properly committed to this though: In practice the US treats Taiwan almost like it is independent, but they avoid calling it that officially. So the US is arguably in breach of its agreement with China on this point, and always was (though I think this was understood by all sides at the time of signing).

In this agreement, the US also promised to work towards reunification and to demilitarize Taiwan. They did in fact remove US troops from Taiwan and scaled down weapons deliveries. Lately though, they are increasingly breaking these promises with more weapons deliveries, more US military personnel on Taiwan, and open support for pro-independence positions and politicians.

The PRC for its part promised to work towards peaceful reunification and not use military force. So far they haven't, so this is currently a one-sided breach of the agreement by the US. Why is the US breaking an agreement that so far has prevented a military conflict?

Both Beijing, as well as the majority of people on Taiwan, are in favor of continuing the status quo for a while longer. But Beijing has made it clear that they will not accept Taiwan declaring independence, and they certainly do not want a hostile military presence so close to the Chinese mainland and important port cities. The PRC has threatened to blockade/invade Taiwan if independence is declared or if there is a military buildup.