Please stop making terrible comparisons. Taiwan, whether you call it after the landmass or after its official government name dating to 1913 or Formosa for all I care, is a sovereign nation that has control over its economy, currency and foreign relations and does not answer to any other higher administration. All these things make it an independent country, not an autonomous region. The PRC is also a country that exerts control over territories that it forcibly overtook making it at least at its inception, an illegitimate government. That was normalized over the course of several decades but it is ridiculous to assume it is a legitimate government in lands that it never controlled either de facto or even de jure since many of its claims are were not part of China either at the time, presently or ever (like the South China sea if you don't like the example of taiwan). PRC and ROC are 2 different legitimate governments of the areas they control. Both are accepted by various members of the international community. To call one or the other the sole legitimate government of ALL that land is playing on favoritism and just plain wrong, historically, politically and diplomatically.

There is no official stipulation within the UN community that would preclude Taiwan becoming a member as a representing body for the ~30 million people living on that Island, as all the treaties from the past do not specify Taiwan and Mainland China as one integral Chinese administration. Please read up on the Taiwanese situation, you really need to.

As for "warping the world to my own preconceived ideas.", I'm not the one grasping at straws, continually making nonsensical comparisons which do not in any way reflect the complicated diplomatic situation of East Asia for the past 70 years to support any "preconceived ideas".