Why does China think Taiwan is theirs?

It was explained to me by a (mainland) Chinese friend as such.

"In some families there is a child, a son or a daughter, who breaks away from the family and does its own thing. They do not want help from their parents, they do not want control from their parents, they only want to make their own way in the world. China is that family and Taiwan is the rebellious child. We may argue, we may not speak for a long time, we may disagree on many things, but we still love that child and we would still take it back into our home if it ever asked". (paraphrased, of course)

Now, this may not be the way the Chinese government see the situation, but it seems that is how the people tend to see it. In broader terms, China still sees a lot of places that were once under the control of the dynasties as still being Chinese. We're seeing a growth in the term "Greater China" as an (allegedly) non-threatening way of referring to the People's Republic, the Special Administrative Regions and Taiwan, as opposed to "Mainland China" for the part that most other countries politically view as China.

China thinks that whatever is written in their very very old map is theirs. Without realizing that many things are changing, some of those islands were already bought, and some people doesn't wanna be controlled by somebody anymore. But still, they will insist it is still theirs because they have an old map as a "proof."

1. Throughout the years, there have been large Chinese territory that got taken away by Russia. Even as recent as in 1999, Jiang signed away and gave up historical claims of large territory that China was supposed to take back after WWII. For example, there was agreement that Vladivostok area was supposed to be returned. But Jiang gave all the rights up. Most of the PRC China nationals didn't even know about these, and had no say about it.

2. Part of the Korean peninsula was a part of Han dynasty territory. Wouldn't PRC take that back because was "child" of theirs?

3. Mongol empire used to rule entire China in Yuan dynasty. Yuan was once the center of the Mongol empire. Wouldn't Mongolia take China back as their "child"?

4. Hitler claimed Austria was theirs, and found excuses to invade Czechoslovakia? Russia says East Ukraine is their "child", and love them so very much?

Here are more facts:

After Mao took China in 1949, Mao wanted to take Taiwan in 1950 to have complete defeat of Chiang, so that Chiang and the nationalists would not have a chance to return to power. But because of the breakout of Korean War and US sent in 7th fleet, Mao had to change plan.

Before breakout of Korean war, Kim went to Mao to ask for help. Mao gave Kim 3+ divisions of PRC's Choson ethnic military to join N. Korea military wearing N. Korea uniforms. Later, when US and UN troops got close to Yalu river, PRC came up with internal propaganda to justify sending troops to cross the Yalu river to fight the Korean war:

. US' protecting Taiwan.

. US jets crossed Yalu river and fired on PRC civilians.

Since the Korean war time, they haven't changed those claims. PRC CCP in elementary school second grade teach their kids Taiwan is theirs. The foreigners get consistent answers when talking to PRC China nationals and think must be true.

In PRC, their people don't have freedom of speech, press, media, etc. They have one and only standard textbook published by CCP. They have "central propaganda department". They have state controlled and run media. They enforce internet censorship. They put dissidents in prison.

The CCP history book is full of partial facts and distorted history, to serve CCP. Today their own nationals when going overseas know to buy books from outside. People ought to check with Stanford university for the project regarding "gaps" of different textbooks of the same period of history.

I hate to elaborate long history on Y!A. This is not the place for it. So here is short version.

Formosa had aboriginal activities for 5,000 years that can be verified. There are museums and historical sites in Taiwan that you can go pay a visit.

Formosa even before was taken by Dutch in 16xx, had its civilization and its kingdom. It was not a part of any other country.

Then there was Dutch in the South who taught the locals about Dutch length/weight measurements and how to trade. In the North, there was Spain (there is still Spanish fort in Tamsui). Dutch and Spanish coexisted with the local aboriginal kingdom. Japan also set their foot there and tried to collect taxes from the locals. Then at the end of Ming dynasty in 1662, there was Ming's general Cheng who had small regions in Taiwan. Then there was Qing dynasty who set up government office but didn't have full control (see 1874 incident Qing deneid they had full control over Taiwan). There was also French invasion; followed by Taiwan got ceded to Japanese for 50 years.

Before Japan took Taiwan, Taiwan sought for help from Qing to fight with Japan but was denied. In 1895,Taiwan declared independence with its own country's name "Republic of Formosa" and its own flag, and fought with Japan but lost. Japan then ruled Taiwan for 50 years.

After WWII, US was the occupying force of Taiwan and Taiwan was returned to ROC and never PRC. Chiang and nationalists moved over to Taiwan. For one time, it was said there were more than 2 million people moved over. Per latest government info, it was 1.21 million, or 13% of the population at the time.

It's 21st century, in Canada, UK, Spain, people use referendum to decide their future; but PRC has 1,400 missiles in range of hitting Taiwan. And in today's world, there is no such thing as who is whose "child".

So if Chiang and nationalists went to New Zealand, then New Zealand is PRC's? Some PRC nationals even say that after 1945 Chiang didn't take Okinawa and therefore Chiang was a traitor.