I don't know too much about the history of China and Tibet, but I seem to recall that the relationship is much more complicated than "Tibet has been part of China for hundreds of years". The Mongol empire is not China just like the Ottoman empire is not Turkey. It doesn't look like the Ming Dynasty controlled Tibet, and the Qing Dynasty was Manchu, not Han. In addition, in 1912 the Chinese army detachments in Tibet simply left and went back to China. The fact that China (and Britain) didn't recognize the independence of Tibet doesn't mean that China did anything to assert authority over it until it got into Mao's head.

Culturally, Tibet has features both from the Hindu and Chinese cultural matrices - like (the perhaps aptly named) Indochina, it's a buffer state between India and China. It is probably not properly part of neither. Someone mentioned the fact that the 3 great Chinese rivers start in Tibet. In fact, they start in the provinces of Amdo and Kham to the Northeast, which China annexed around 1928 leaving the region around Lhasa (what is now the Tibet Autonomous Region) alone. The region around Lhasa is an endorheic basin with no ecoregion-level connection to China proper. Someone mentioned the sources of the Brahmaputra but that's just on the southernmost edge of the Tibetan plateau. Were it not for the buffer state location between China and India it would have no strategic value to China. Well, maybe there are some mineral deposits there. At the rate they're going China can rape those resources in 5 years and move on to greener pastures leaving a bunch of smoking holes in the mountains. Which brings me to the PRC as "history's most successful poverty reduction program" to quote another comment of yours in this thread. Is that sustainable? It's being done at an appalling environmental price, and it is doubtful that the Chinese people in the hinterland are benefitting at all from it, not to speak of the fact that the Cultural Revolution was a cultural suicide to follow the physical suicide that was the Great Leap Forward. Wasn't there some story about all metal objects being confiscated in order to help the industrial production, but for instance the many, many tons of steel produced to match the insane targets of the central planners were brittle and effectively crap steel? What a waste.

Tibet fun fact of the day: the game of Go (WeiQi in Chinese, quite possibly also the game referred to as Qi in ancient texts) probably originated in Tibet. We know this because an archaic version of the game is played there. Maybe we could have a case of "our national game originated in Tibet therefore Tibet is China".

It'd be nice if the battle were only against the right wingers, not half of the left on top of that — François in Paris