Things would be simple if it was just
Taiwan wanting to be
independent, but that's not it.
The Chinese think that Taiwan is a rebel province they need to get under control, but the Taiwan government thinks it should be the ruling government of China. The United States and the United Nations would not even recognize communist China until Richard Nixon went over there and worked things out. This caused Taiwan to be booted off the Security Council and the 1 billion people of mainland China finally got a voice in the U.N.
Sure, things have changed over the last 50 years but this is the basis of the conflict; two groups wanting to control the same place.
I'd be happy if Taiwan would just declare independence. Then we (the US) could officially support them (they'd be a democracy under siege by Communist oppressors) and maybe we'd get some deals on importing all of their computer products.
But it's none of my business...