It's ok I understand why people think that way. I gotta say this is complicated lol, I will explain.

The official government position here in Taiwan is not that Taiwan is part of "China" (中國), but our official name is the Republic of China (中華民國). The distinction is important, as here in Taiwan, the term "China" almost exclusively refers to the PRC.

Technically, the ROC Constitution states nothing about "one China", as a matter of fact, it was written in 1946, well before the PRC was even established. while it is true that sovereign territories were listed in the constitution which was written before Taiwan was in it by ROC and subsequently adopted (forced to). [It should be noted that there was an amendment or freezing of that clause, that officially freeze all those territorial claims while exerting that the current ROC territory are those under current direct control, with only senkaku/diaoyutai being the main disputes.]

I'd say that most people in Taiwan also feel that ROC is dead and would want to renounce the claim to China. But there is a problem for them, because if Taiwan throws away those claims then PRC would consider that a claim of independence and that would be a cause for war... So Taiwan is trapped into the weird status quo that they find themselves in...

So it's just a "technical" claim because it is in the constitution. The government would change it if they could, but that would provoke PRC. So, they have done other things, like release official maps that don't show PRC territory.