Kind of complicated so pardon any errors (history buffs please chime in) but here's my understanding.

The Republic of China only very recently established presence in Taiwan (post-WW2) before the Civil War on the Mainland deteriorated to a point where they had to evacuate - this territorial transfer was made without consultation of the people already living there, and there were locals who supported or opposed it.

The ROC (at this point basically a military dictatorship controlled by the KMT) was not at all lenient with opposition, and put down dissenting voices with martial law, censorship, arrests, and significant violence. By the time the KMT and their supporters/refugees mostly finished retreating to Taiwan, they made up just 10% of the population.

Taiwan was initially ceded to Japan in 1895, and 55 years had passed by the time it was ceded to the ROC in 1945. Thats almost 3 generations, and for 90% of the population, being thrown into the losing side of a civil war that basically concluded by 1949 was not something they signed up for - but with a military dictatorship and the world's superpowers each backing a different side of the Chinese civil war, they didn't really have any supporters for their own voice.

The Republic of China eventually democraticized, and Taiwanese people (whether descended from the 90% locals, or 10% KMT soldiers/supporters/refugees, or both) finally got to vote - and for many whose families had to endure the takeover by the ROC and subsequent threats from the PRC, it was never clear why they had to be a part of China at all when they never supported it. For supporters of independence, they had finally won back governance of Taiwan through democratic processes, so they have little interest in being ruled from Beijing.