There are a variety of reasons, but one of the main ones is on the issue of territorial legitimacy. Imagine if during the U.S. Civil war, the Union conquered all of the South except Texas for some reason. Then instead of trying to reconquer Texas, they just give up and say "oh well, I guess ya'll can be your own country" and just let Texas succeed from the Union. At that point the United States have basically announced to their entire country that they will legitimize separatist movements, which not only will create new separatist movements and strengthen existing ones, but it would also undermine the entire endeavor of retaking the rest of the south in the first place by basically telling them that they could've gotten away with succession.
So when it comes to Taiwan, the island was a territory of China starting in the Qing dynasty, and is currently being run by the government that lost to the communists during the Chinese Civil war, but also with the added dimension of it being protected by a foreign power in the form of the US. So given the situation, China acknowledging Taiwan as an independent entity would not only give a lot of legitimacy to other separatist movements in China (Tibet, Xinjiang, etc.), it could also be seen as a green light for various imperialist or colonialist powers to come in and potentially try and seize Chinese territory for themselves without much backlash from the Chinese government.
TL;DR: Any country that acknowledges a separatist movement, especially without losing a war to said movement first (ex: how USA gained independence from British), immediately throws ownership of the rest of its territory into question and makes the government look weak.
There are a variety of reasons, but one of the main ones is on the issue of territorial legitimacy. Imagine if during the U.S. Civil war, the Union conquered all of the South except Texas for some reason. Then instead of trying to reconquer Texas, they just give up and say "oh well, I guess ya'll can be your own country" and just let Texas succeed from the Union. At that point the United States have basically announced to their entire country that they will legitimize separatist movements, which not only will create new separatist movements and strengthen existing ones, but it would also undermine the entire endeavor of retaking the rest of the south in the first place by basically telling them that they could've gotten away with succession.
So when it comes to Taiwan, the island was a territory of China starting in the Qing dynasty, and is currently being run by the government that lost to the communists during the Chinese Civil war, but also with the added dimension of it being protected by a foreign power in the form of the US. So given the situation, China acknowledging Taiwan as an independent entity would not only give a lot of legitimacy to other separatist movements in China (Tibet, Xinjiang, etc.), it could also be seen as a green light for various imperialist or colonialist powers to come in and potentially try and seize Chinese territory for themselves without much backlash from the Chinese government.
TL;DR: Any country that acknowledges a separatist movement, especially without losing a war to said movement first (ex: how USA gained independence from British), immediately throws ownership of the rest of its territory into question and makes the government look weak.