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A simple analogy to understand the Korean War
Imagine sharing a distressed childhood with a sibling. You were extremely close since he/she was the only family you knew, and also because you were fighting against an external force. That evil force finally disappears, but with it, also disappears unity. Your sibling acts strange and starts to make friends that you cannot stand. The distance between the two of you grow, and you feel betrayed. To get the sibling to accept your own rules so that you can become close once again, you two fight, but to the point that you almost kill each other.
I understand that this is bit of a stretch, but you get the sentiment, and why the relationship between North and South Korea is so complex.
Very briefly: Korea was one country for a very long time, and in the beginning of the twentieth century, was occupied by the Japanese. After World War II, Korea was liberated, which created a power vacuum. The USSR and USA supported different political powers, and did not leave the Korean Peninsula right away amidst the Cold War. Two new governments were created, one democratic (Seoul) and one communist (Pyongyang), and shortly thereafter, North Korea invaded South Korea to unify the country by force. Three years later, they signed an armistice.
Fast-forward sixty years, and here we are. How sad.