Both ROC and PRC are claiming mainland China and Taiwan as their exclusive territory. You can't acknowledge either claim without essentially dismissing the other in its entirety (which is just a polite way of speaking of war). At the same time, neither party can acknowledge the other side, because of this. Any attempt to resolve this by means of a regress will result in an infinite circle. Hence, everybody is tiptoeing on hot coals…

(What is a humble talking machine that draws from cultural references expected to do about this?)