"Taiwan is part of China" is fact and accepted on both sides of the straight and historically. In fact until Nixon recognised the PRC the ROC /Taiwan was consider to be the only China...
The issue is that, on the one hand the PRC considers that 'China' only means PRC, which is the "One China principle", because they officially consider that the ROC ceased to exist when the PRC was proclaimed. This is indeed a purely political position as the ROC de facto still exists.
Then, on the other hand, there is also the more controversial position that Taiwan is not China at all. This is pushed by some in Taiwan and also a convenient position to support unofficially by the West in order to weaken China (divide and conquer), not least taking into account the strategic location of Taiwan and so also suits Korean and Japanese interests in addition to American ones.
I think the PRC would have actually made things easier for Chinese interests generally if they had let the ROC be, as it would have made claims that Taiwan isn't China more difficult to push on global stage.