I think all three countries have arrogance for different reasons. Keep in mind though that I don’t think Chinese/Koreans/Japanese are overall very arrogant; I find Americans to be generally the most arrogant out of all people I’ve interacted with.
Chinese have a lot of pride in their 5,000 year history. Many Chinese will mention that Chinese written history goes back to the Shang Dynasty. Only Greece and Egypt really rival China in terms of history. China was the pre-eminent superpower in the world for over 1000 years, especially during the Middle Ages. Until Europe reached the Renaissance, China especially during the Tang, Song, Yuan and Ming dynasties was incredibly powerful. These days China is an emerging superpower still trying to shake off the disaster that was the Cultural Revolution which pushed back their development by about 100 years.
Koreans are historically quite closed and modest. They are one of the few countries that never had imperial ambitions or tried to invade another country in its history. Modern day Koreans may think they are superior to Chinese and other Asians because of the strength of their economy, entertainment, fashion and other soft influence power they have over the world which at present time is superior to Chinese/Japanese soft power.
Japanese had the most success in their history after (ironically) Americans forced them to open up in the 1850s and they were the first Asian country to industrialize. This gave them an added technological edge over other Asian countries that allowed them to conquer Korea, and a very weakened Qing Dynasty China (which previously had to fight off Western powers in the Opium wars). Japanese arrogance stems from this colonial period. They were able to take over Manchuria, Korea, Taiwan and the military was probably the most advanced in the East. Of course, they met their match when they tried to attack the USA. Modern day Japanese influences the world with their technology and animation but overall I would consider their influence to be declining compared to China and Korea.