And Taiwan claims the mainland, Mongolia, larger portions of Manchuria than even the PRC claims and has overlapping claims with the PRC in the South China Sea.

And Taiwan claims the mainland, Mongolia, larger portions of Manchuria than even the PRC claims and has overlapping claims with the PRC in the South China Sea. The Republic of China Constitution makes it clear they consider the Mainland Provinces to be part of the Republic of China. After many decades of domination by Japan and Western powers it's understandable that many leaders in the ROC want a status quo ante with regard to mainland China. Whether one agrees with their stance or not it is certainly understandable why they think the way they do. The US doesn't officially recognize the ROC but it does maintain a military presence and agreement with the ROC government. The difference is there is a large fraction of the population in Taiwan that is willing to trade away all of those claims including their claim to the name of China and become an independent State outside of China.