There are a large number of things that are factually incorrect with your position.

1. Taiwan is a small island off the coast of China. By virtue of its size, the coastal waters of mainland China contain the island of Taiwan. By virtue of its distance from the mainland, if the island were not present, off the coast of the mainland includes off the coast of Taiwan. The island of Taiwan is about as far from mainland China as Key West is from Florida. Activities off the coast of Key West are considered activities off the coast of Florida and not of some other state.

2. The nation of China has included the island of Taiwan from centuries. When two different political groups fought a civil war for control over the nation, the losers fled to the island of Taiwan and declared themselves the government of the nation of China in exile. At no point did either group decide that the mainland and the island were part of different nations or nations unto themselves.

3. The historical reason many nations have distinct relationships with Taiwan is historically relevant here. The reason is because most nations were anti-communist, refused to acknowledge the communist government of China, and still wanted to exploit China. So, they recognized the KMT as the government of China - not of Taiwan but of China, because the nation of China includes Taiwan. The reason they did this is because they had been dominating China for 100 years and believed the KMT would act as their vassals and believed the CPC would not. So, imperialists who were dominating China protected the losers in the civil war. Had they not intervened, the losers would have been captured. UK and USA creates a dependent puppet government while it conducted a mass murder campaign for decades. All the whole, no one said Taiwan was a separate and new country, not even the KMT on the island of Taiwan.

4. The UN has a seat on the security council for the nation of China. The KMT was the political body occupying that seat on behf of the nation of China. When the CPC won the war and took over the nation of China, the UN continued to assert that the KMT was the rightful government of China, the nation that includes the island of Taiwan. Eventually, no one could sustain the bullshit anymore and the CPC, the political group in charge of the nation of China, took the seat at the UN.

Thus, the world sees Taiwan as a province of the nation of China and the CPC as the political government of the nation of China. The people of Taiwan, that is to say, the survivors of the 40-year reign of terror where it was a crime punishable by death to even talk about the CPC as the government of China, some of these people now wish to figure out a way to secede. Why do they wish to secede? Because the UK and USA have invested decades and trillions and in creating conditions that make this a reasonable position. Like Hong Kong, the West has established significant finance capital and high tech operations that give an elite upper crust a very high quality of life and the middle class a quality of life like a wealthy European nation. In addition, the West has spent 40 years propagandizing and manipulating the people on the island under the banner of protecting the KMT from the evil commies.

So yes. There is a secessionary movement. It is explicitly motivated by desire to be economically dependent on the West. But it is a secessionary movement to become something other than a province of the nation of China, which means it assumes from the get go that Taiwan is not an independent nation.

Your utter lack of historical understanding is appalling, especially in light of your position that military response by the West is justified.