There's some irony in that the KMT originally wanted to rule China but were driven out by the Communists, so they fled to Taiwan and established a one-party state there. The DPP finds core support from the indigenous island population who resent the KMT and mainland influence, along with those who don't want to join China for other reasons. The modern KMT is owned lock stock and barrel from Beijing and is now an agent to bring Taiwan under central Party rule.

The DPP really wants Taiwan to be an independent country and one aspect of that is formal recognition from the UN. China is desperate to prevent it, because China wants to assimilate Taiwan as a province. It's very unlikely that Taiwan will be recognised at this time.