It was part of China during the Qing dynasty since 1750.

They declared independence in 1913 after the fall of the Qing but it was not recognized by the Chinese Republican govt.

The PRC re-annexed it in 1951.

By that argument the UK could re annex parts of France and the USA.

And Italy could take back large chunks of the near east.

Conversely, if not for that argument, China would be a hodgepodge of local warlords (what it was post Qing, before ROC's unification). A problem of claims by irredentism is what time period do you consider the proper extent of a nation's territory?

This applies to both the rationalisation of Tibet belonging to China, and for not belonging.

Good question.

If you can't force the issue (i.e Yugoslavia, Kosovo, Cyprus, Crimea) via a force of arms or diplomacy.

Their independence lasted 39 years and was not recognized by the new central govt which had bigger issues to deal with.

Calais was lost in 1558 and UK monarch stopped using the title "King Of France" in 1800 so it is a settled issue.

And Corsica was part of Italy (or italian states at least) for 5 centuries and only part of France relatively recently. According to your logic it should return to Italy?

If it was part of Qing, and Qing fell, why should Chinese Republican govt and/or PRC have any say in the matter?

ROC took over the assets and liabilities of the qing, just like russia did with the soviet union

What liabilities did the Russian oligarchs take on?

existing treaties with china, us, plus nuclear arsenal etc.

PRC, ROC and Tibet can claim all the rights it wants, but buddy, you have to back it up militarily and politically.

how about texas and mexico?