you can but it's not correct!! :-) You are Taiwanese. Like Chinese, Japanese, Nepalese, Portuguese, etc. etc. I am Australian. I am not Australianese or Australianish!

where is no "why" in vocabulary it's only correct to say "Taiwanese"

I can say I'm British or I'm a Brit. But some countries are offended by shortening of their name. Such as Pakistanis. Other countries use completely different slang terms - Americans can be called Yanks. With political correctness creeping in, some terms are no longer appropriate to use, such as Indians being used for Native Americans. If most of your population started using one of your terms then it would become acceptable and used by most. It is how language develops and adapts over time. Some words are added while others are removed. Ye olde English is seldom used anymore, but is still understood by most.