Taiwanese were resistant because the mainlanders were not friendly arrivals. When the KMT moved to Taiwan, they pretty much immediately turned into an authoritarian regime. Essentially, this was a colonization project. Mainlanders moved to Taiwan, and the new KMT government enacted policies that were harmful to Taiwanese people. For example, for decades Mandarin was made the official language at the expense of the traditionally spoken languages such as Hokkien and Hakka. These languages did not die (today, around 80% of Taiwanese people speak at least some Hokkien and Hakka at home), but there was still an effort to stamp them out. The country was under martial law for the most of the time that the KMT occupied Taiwan, up until democratization in the late 1980s, and that period was bad for non-mainlanders. It's referred to as the White Terror. I say this was a colonization because the mainlanders came from a different region of China historically and attempted to get rid of the Taiwanese society that had been developing for hundreds of years by immigrants from Fujian in favor of their own vision. It was an occupation by a foreign entity in reality. Taiwanese people were excluded from politics, and generally the mainland arrivals supported the government and its determinations about what constituted "Chinese culture", since it was their own colonial culture. These policies ignored the fact that Taiwanese culture itself was based on the diverse cultures of China. Saying that one's ancestors are not tied to the KMT is a way of saying they are Taiwanese, not Chinese, a 本省人 běnshěngrén ("native" of an area; not to be confused with the term used for the indigenous population) not a 外省人 wàishěngrén (an outsider). Even today, after decades, descendants of people who moved from the mainland are still often referred to as 外省人. Really, the KMT became the ruling party due to force, and mainlanders were not seen as friendly arrivals because the KMT attempted to replace Taiwanese society by force, at least at first.

I think a good introduction for all this is Why Taiwan Matters by Shelley Rigger. It's kind of a little overview of Taiwanese history and good for an introduction to Taiwan. I think on top of that you should probably look at Is Taiwan Chinese? by Melissa Brown because it makes an argument that Taiwan has developed a distinctly different culture than the mainland over the years.