IIRC, it's because the mainland Communist Party's domestic propaganda pushes the line that the Chinese people aren't ready for democracy, in order to legitimize its authoritarian rule.
The fact of Taiwanese democracy directly disproves that. They're a very similar population separated by only 70 years of political independence (and the democratic changes were only in the last 30 years, IIRC).
"The ethnic groups of Taiwan may be roughly divided among Taiwanese (84%), mainland Chinese (14%), and indigenous peoples (2%). The ROC government reports that over 95% of the population is Han Chinese, which includes Hoklo, Hakka and other groups from mainland China."
So I guess "Chinese" is a shortcut for "Han Chinese"
Now, to be clear, Taiwanese don’t consider themselves Chinese in the CCP/PRC sense. It’s tantamount to calling Canadians Americans.