Thank you for listing me as an example of an intelligent person, but you also insult me as an ignorant person who is brainwashed by the Chinese government. Without checking history, you automatically assume I take my stands on Taiwan because I was brainwashed by Chinese government instead of me doing my research and forming my own opinion. I can assure you, I'm not brainwashed at all. I know a lot about Chinese government propaganda, AND western propaganda. Oh yes, every government broadcasts propaganda. If you think your western government tells you the truth nothing but the truth, you're delusional.
Now, let's talk about Taiwan history. Because China's claim to Taiwan is based on an historical claim.
Taiwan, by itself, was (and still is) an insignificant small island with very limited natural resources and primitive indigenous people. Taiwan was first colonized by Dutch and Spanish colonists. Later the Ming admiral Zheng Chenggong attacked Taiwan and took the island as part of Ming Dynasty in 1662. In 1683, the entire Taiwan island became part of Qing empire, first as part of Fujian province, later as its own province. Since then Taiwan had been part of China for over three centuries until in 1895 China lost the first Sino-Japanese war, and as part of postwar repayment to Japan, Taiwan was ceded to Japan as its colony in the Treaty of Shimonoseki, an unequal treaty forced upon Qing government by Japan.
If Taiwan was never part of China, how could the Qing government cede it to Japan? You can't cede an independent country to an other country. You cede your own territory to another country.
After losing World War II, Japan lost Taiwan as well. And the island was returned to the Chinese government. By now, however, the people in Taiwan had become quite fond of Japan's rule and some of them weren't happy with being taken back as part of China. Partly because Taiwan being the first oversea colony of Japan, Japan wanted to set a good example for its other (possible) future colonies. Not only Japan didn't commit much mass murder like it did later in mainland China, it actually helped Taiwan with a lot of infrastructure construction, set up schools (teaching Japanese of course) and was generally quite nice to Taiwan. That's why a lot of Taiwan people had fond memories of Japan occupation even they're second class citizens. While the corruption of the new Chinese government didn't help the situation, and there're a few rebellions breaking out.
After three years of civil war, Chiang Kai-shek ran and took Taiwan as its base of operation, that had started the long history of separation of Taiwan and Mainland China.
As you can see, after Ming dynasty took Taiwan, and with the sole exception of Japan occupation, whatever happened in Taiwan was China's internal affairs. Taiwan has been part of China longer than US has been a country.
I'm talking about solid, record history. There's nothing "propaganda" about it. China has the historical claim of Taiwan, Taiwan has always been part of China. And due to political differences between two parties, now Taiwan is an autonomous province. ROC want to be independent because nationalist party wants to hold against communist party. I could say it flamed the Taiwan independence movement. I could say Taiwan independence is a product of political propaganda. US plays a role in this political struggle because it wants to keep an foothold in Southeast Asia sea, to keep China under control. If you think US helps out Taiwan because it believe in democracy and some such idealistic crap, you're 图样图森迫 (too young too simple). Every major power involved in Taiwan issue want something of their own, it has very little to do with regular Taiwan people.
When I say Taiwan belongs to China, I don't mean Taiwan belongs to the Communist Party. If you ask me, the Communist Party shouldn't own mainland China, let alone Taiwan. I believe Taiwan belongs to the political, cultural, and geographical entity known as China. If there's a political revolution and some new government has replaced the Communist Party to represent China, this new political entity (totalitarian or democratic) would inherit the claim on Taiwan.