They also claim that the Taiwan-island is part of their territory. Since Its currently full of taiwanese people and China holds regular military exercises around that island an invasion does not seem far-fetched.
The CCP takes a long view of things. They know the diplomatic fallout from the invasion will subside eventually, so they're less worried about "global concern" than you might think. It's likely they would have done the invasion already but for the fact that invasions over water are really difficult and they're not sure it would succeed.
