Briefly, China lost to Japan in 1895 gave Taiwan and nearby islands to Japan.
After WWII, US assumed control of the islands and two Chinese parties Communist and Kumingtong fought a civil war. Kumingtong lost and retreated to Taiwan in 1949.
In 1971, the US gave the islands to Japan at will so that they can continue to maintain their military in Japan to contain communist China and Russia.
Both China (communist) and Taiwan (Kumingtong) did not raise the issue seriously because they want US to recognise either one of them as the official China in order to overtake the other party.
Japan took advantage of the fighting between the Chinese.
Culturally, My experience has been that Japanese people, generally, are the most obstinate people I have ever met and with that obstinace comes a extreme reluctance to admit or take responsibility for their transgressions because they rather save their face then their ass.