Regardless of having China "own" Taiwan, Taiwan has their own government and laws. Therefore, in my eyes and hopefully others, you can't have two different functioning government types without having another country. Taiwan is its own country and rightfully so.
Here is why Taiwan is an independent country. For simplicity, Republic of China will be referred as “Taiwan”, Republic of China will be referred as “China”, and the mainland China region will be referred as mainland.
1. History - In World War 2, China didn’t exist yet, Taiwan was the sole government and ruler of mainland. And Taiwan fought in WW2. Google "Blood Chit” or flags of world war 2, you won’t find any historical picture of China’s flag. Taiwan was the representative county of mainland in U.N.
2. History - After World War 2, due to war Taiwan’s government was weak. China communist took the advantage by rebelling against Taiwan. Taiwan’s government fled to Formosa Island, the Taiwan island. Hence, does Taiwan actually belong to China? Clearly not. Think of it this way, if ISIS rebelled against Syrian Arab Republic (government of Syria) and won, is Syrian Arab Republic part of ISIS now? Or if Canada rebelled against England and won, is England part of Canada? The situation is much the same.
3. International - Currently, Taiwan isn't recognized as a country by UN and many countries. This is because China poses economic threat on many countries who supports the existence of Taiwan. United States, once supported Taiwan, now feels economical pressure of China and can no longer support existence of Taiwan directly. Furthermore, Taiwan lost many of its supporter because China either bribed them or put economical pressure. Regardless if Taiwan is a country or not, perspectives of countries should not be influenced by political, economical and military pressure.
4. Infrastructure - Infrastructure of Taiwan region is well developed in terms of GDP, human rights, political system, transportation, currency, education, technology, healthcare, military and many more. Without taking in consideration of China or how other countries look at Taiwan, please provide a reason why Taiwan cannot be an independent country. People in Taiwan wants to be independent, then you should let them. After all, Taiwan is not a tribal state.