Because they consider themselves to be the original China, since their government was formed from the Nationalist (pre-communist) government of China, who were chased out by the Communists.

The situation is NOT like this:

🇨🇳: The island of Taiwan is part of me!
🇹🇼: No, I am an independent nation!

It’s like this:

🇨🇳: I am the true China, and the island of Taiwan is part of me!
🇹🇼: No, I am the true China, and the mainland is part of me!

Which is why there are some countries that do not recognize the People’s Republic of China (mainland), and instead recognize the Republic of China (Taiwan) as China.

My information from:
en.wikipedia.org/…/Retreat_of_the_government_of_t…
www.taipeitimes.com/News/feat/…/2003660529