Why did both Korean governments in 1948 claim authority over the entire peninsula?

Following the end of World War II and the collapse of Japanese colonial rule, the Korean Peninsula was divided at the 38th parallel by the United States and the Soviet Union as a temporary administrative measure. As Cold War tensions intensified, efforts to establish a unified government through a joint commission failed, leading both sides to solidify their respective zones of influence.1234

In 1948, two separate states were formed: the Republic of Korea in the south and the Democratic People’s Republic of Korea in the north. Each government claimed to be the sole legitimate authority over the entire peninsula because both sought to represent the unified national identity that had existed for centuries prior to the division. Furthermore, each state was backed by a superpower—the U.S. supported the south, while the U.S.S.R. supported the north—and each received recognition from its respective allies as the only lawful government of Korea.42