I shake my head when TW and HK people identify themselves as "not Chinese". Just makes them sound stupid. And mojo, that'd be true if they were indigenous Taiwanese, but indigenous Honkies? No such thing.
The reason that they don't want to be called Chinese is because of their early education, as a kid in primary school, they were taught to hate the communists.
But in a couple more generations, this could change, people should be able to think for themselves.