Why two nations that should be allies cannot get along.
Baird Maritime has a short feature on the background of the dispute between Korea (both North and South) and Japan over 0.072415 square miles of rocks in the Sea of Japan. Also known as the Liancourt Rocks, they are Dokdo to the Koreans and Takeshima to the Japanese. The post also talks about other sources of bad feeling.
The US would very much like to see more defense cooperation between the two, but history and pride keep getting in the way. As an indicator of how strongly the South Koreans feel about this, they named their largest warship Dakdo after the island group.
Japan should take their case to the international tribunal and then accept the result.