(that is the joke)
Taiwan is a small Island/Country/Province(depending who you ask).
A long time ago (like 60 years), in a country far away, two groups battled to control China.
In the end, one group kind of lost, and took refuge on one of the islands that were part of China.
The government on this island, Taiwan, called themself the "Republic Of China" and said they would eventually conquer back the mainland, the government in the mainland called itself "People's Republic Of China".
In the end, the mainland never considered Taiwan a country at all, if you ask there it is a province of China with funny writing.
So, saying "Isn't that the flag of China?" to a Taiwanese is like... well, throwing a big rock / trolling.