It is no secret that Koreans and the Japanese do not have much love for each other. I would say bloody history between Korea and Japan has much to do with it if not everything. Japan attacked Korea a number of times throughout history and killed, tortured, and raped people of Korea.
Koreans are still upset at the fact that the Japanese are not apologizing for forcing Korean women and girls into being "comfort women" for the Japanese soldiers during World War II. (The sex slaves were not just from Korea but from many other Asian countries as well. It explains why Japan is not really a popular nation in Asia.)
But Japan actually did offer apologies to Koreans a number of times. The Japanese government issued statements saying they would like to "declare anew (our) remorse at these deeds and tender (our) apology to the people of the Republic of Korea." According to Wikipedia, the comfort women of Korea were compensated whopping $2,300 USD per person in 1998 by the Japanese government.
So why are Koreans being so stubborn and not letting it go? It is because the prime minister of Japan, Shinzo Abe, keeps saying those Korean women volunteered to be sex slaves. He also has said that Japan did not really invade Korea. (He says that the word "invasion" is very ambiguous.) The Prime Minister of Japan also claims that a Korean island, Dokdo, is part of Japan and not part of Republic of Korea. History textbooks in Japanese public schools basically say the same thing.
Can you imagine the U.S. invading Canada, killing and raping Canadian people, and not owning up to it? Imagine the U.S. president saying how Canadian women wanted to be sex slaves and it was not really an invasion. Something tells me that Canadians and Americans wouldn't get along either if that actually took place.
The relationship between Korea and Japan is not likely to improve anytime soon. Japan is covering their ears right now and glorifying their unforgivable past. But Koreans are not buying it. Neither are the Chinese. (In fact, the people of China appear to detest the Japanese even more than Koreans do.)
Japan is like a child who used to bully all the other kids around. But now, all the kids have grown up except for the bully. Maybe it is time for him to finally grow up and find a new identity.