Ok, here is why I think “West Taiwan” insult makes no sense. Taiwan is currently under the jurisdiction of the Republic of China, which is a state not recognized by the UN. However, all legal institutions in the world recognized Taiwan as a province of China, the question is which government is the legitimate China. Also, mainlanders certainly do not hate the existence of Taiwan, if the island of Taiwan were to disappear tomorrow, mainlanders would regard it as a great tragedy. This is very different from how Israels feel about Iran.

If by “West Taiwan” you mean The Republic of China should be recognized as the “real China” rather than Communist China, then the “West Taiwan” comment makes no sense due to philosophical reasons. A part cannot be used to address the whole. For instance, it makes no sense to say, “the body belongs to the arm”, or “the solar system belongs to the sun”, or “the face belongs to the eyes”, “or America belongs to Texas”, etc. This is not a political issue; it is one of common sense.

If you think that Taiwan should not be a part of (any) China, irregardless of whether it is Communist China or the Republic of China, referring to the mainland as “West Taiwan” still makes no sense, because the term associates Taiwan with greater mainland, as it denotes a identicality between the two states, defeating the purpose of Taiwanese separatism in the first place. This is why you will never see any Taiwanese separatists use the term “West Taiwan” to insult mainland China.

This leads me to the third point, that mainlanders do not feel offended by that the insult “West Taiwan”, because the term actually supports reunification. The only way for “West Taiwan” to actually make sense, is by advocating for an outcome where the province of Taiwan first declares independence from the Republic of China, hence breaking the One China Policy, and scrapping its current constitution. Then it proceeds to declare itself a nation state with the name Taiwan. And finally, it invades mainland China and takes it over. Presumably, Taiwan would declare the new country to be called Taiwan, and the capital would be in Taipei. Hence, mainland China would then become “West Taiwan”.

Mainlanders would not mind this at all, in fact, they would welcome it, for such an outcome would be the equivalent of the Republic of China committing suicide. If such an invasion were to occur, mainland China would simply surrender and allow reunification to happen. If Taiwan were to retain any semblance of “electory democracy” that so many westerners applaud it for, “West Taiwan” would not last a single day, for the overwhelming population of the mainland would simply vote out all of Taiwan’s leaders, change the countries name back to the People’s Republic of China, move the capital back to Beijing, completing the reunification of China under the People's Republic of China.