The reason why the Pope sent a letter to Goryeo : Empress Gi.

In 1333, Empress Gi went to Yuan (Mongolia) as a princess and became a court lady. At that time, Goryeo was under Mongol rule and sent a certain number of virgins to Mongolia as princesses each year. Most of the princesses who went to Mongolia entered the palace and became court ladies. Empress Gi was so beautiful and knowledgeable that she became the concubine of King Hyejong of Mongolia. She gave birth to her son Ayushiridara and became empress. Her son Ayushiridara later became emperor. 

The exact reason why the pope sent a letter to Goryeo has not been revealed. However, there is a hypothesis that it was necessary to establish diplomatic relations with Goryeo because Empress Gi, who came from Goryeo and became empress, grew in power. In fact, in the East, when an empress came out of a family, all the people from that family assumed important government posts. 

On the contrary, the people of Empress Gi's family, who remained in Goryeo, came to have tremendous power. At that time, the king of Goryeo was King Gongmin. He implemented various reform policies to escape Mongolian interference, which was opposed by the people of Empress Gi's family.

In the movie "The Frozen Flower" King Gongmin appears as a gay man. And killed by his own men. This is all a novel. Song Ji-hyo, who plays Queen in the movie, is a Mongolian princess. At that time, there was a custom in which Mongol princesses and kings of Goryeo married. The princess who married King Gongmin was Princess Noh Kuk. She had a very good relationship with King Gongmin. She is famous for stopping the assassination by throwing herself just before King Gongmin was killed by an assassin sent by the opposition. However, since there were no children among them, there were rumors that King Gongmin was gay, and writing this as a novel was a "The Frozen Flower".

King Gongmin tried to remove the family members of Empress Gi and gain independence from Mongolia. It is true to some extent that he removed the Empress Gi family from the film. However, when the princess died, he fell into deep sorrow and lived a life of depression. Later he was assassinated by opposition parties.

Since then, Mongolia's power has weakened, and the kings of Goryeo have initiated reforms. But failed by opposition forces and the country became increasingly chaotic. Opponents of reform were very corrupt and accumulated wealth through large farms. It was natural for them to oppose reform. Eventually, Goryeo was destroyed by a general named Yi Seonggye. Yi Seonggye was a general of Goryeo and established Joseon.

P.S. It is true that King Gongmin has an escort unit of young men. There is also a story that King Gongmin went crazy and became gay after the death of Princess Roguk. It's also true that he was killed by his guards. However, it is not clear whether the guards betrayed King Gongmin and cooperated with the opposition, or whether King Gongmin was actually killed while engaging in gay acts. The claim that the opposition created a cause after assassinating King Gongmin is more convincing.