Why do they want to be free of China? They have religious freedom and speaking of the Tibetan Buddhism, believe or not, it's so popular in the whole China. There's one big Tibetan Buddhism Temple in Beijing, the capital of China, which was built by one of the Emperors of Qing Dynasty.
They have always been Chinese, ever since the very beginning, on that land, long long before your ancestors were born. And now when the current government supplies so much money, builds railway for them, some of them want to get rid of China?
What are they thinking of?
Speaking of spiritual leader, besides Dalai Lama they also have Panchen Lama, right there in Tibet, in China.
Yes, they're not violent and they won't wage war to get the freedom, so the separatists caused disturbances to kill han people, even Japanese and Koreans just because they look alike.
Maybe they just hate han people. Without any reason.