Tea was a popular drink in Korea during the Goryeo dynasty, which reigned from 917 to 1392. But the beverage's popularity declined in the Joseon era from 1392-1910, until it began to bound back significantly in the early 19th century.^1 I'll explain why it declined.

The Goryeo court practiced state-institutionalized Buddhism, and tea was a beverage associated with this Indian religion and particularly Zen Buddhist practice. There were even towns that existed mainly to provide tea to monasteries and temples, and between Buddhist institutions there were competitions to make the better tea. Tea was also associated with court practice, but what's important here is its connections to Buddhism.

Enter the Joseon. Although the Joseon elite was IMO a continuation of the Goryeo elite, this new generation of Korean aristocrats increasingly rejected the state's Buddhism and sought to implement the newly introduced Neo-Confucianism within the peninsula. So in the early to mid Joseon era we see a lot of edicts seeking to change and Confucianize Korean society, which is discussed in The Confucian Transformation of Korea.

Tea being tied with the Buddhist institution, the beverage's fortunes fell as the court grew much less supportive of the religion and many Buddhist temples and monasteries fell into disrepair. The drinking of tea continued to some extent in the court and among the aristocrats (the cultural shifts of the early Joseon era were gradual) but by the 16th century the court largely stopped drinking tea except in special occasions (the greeting of Chinese dignitaries, for example), and the delicious drink had properly survived only among certain Buddhist circles. The decline of tea was also tied to increasingly colder temperatures, which made the growing of tea unproductive even in more southern areas of the country. So by the wars with Japan in the 1590s, the Korean king would tell the Ming general that "Korean custom" was to not drink tea, ignoring Korea's tea tradition that had flourished only a few centuries before.

Source:『한국의 다문화』by 김운학

^1 Just to clear this up, this was an indigenous development with nothing to do with the growing power of the West. The 19th century revival of tea owes much to "the Eulogies of Eastern Tea," the only traditional Korean tea guidebook which was written by the Zen monk Choui in the 1830s. The phrase "the Dao of tea" began to be used in Korea for the first time in the early 19th century as well.

Edit: Corrected errors