I see you've failed to read the article, got mixed up on the title, or both. China's jets ended up in Taiwanese airspace.

Taiwan's sovereignty is complex: the very existence of the People's Republic of China means that Taiwan isn't part of them. It's the last little extant bit of the Republic of China from before the communist coup. Taiwan doesn't necessarily want the rest of China back (fair enough - it's got communist stink everywhere) nor do they want to become part of China (and judging how craptastic China is doing with Hong Kong these days, there is NO path to Taiwan joining China). So, their only option is to be a sovereign state by themselves while a neighbour continuously says: your country is technically ours.