Liancourt Rocks dispute

I'm interested in Liancourt Rocks dispute between japan and Korea, because I find many topics (nationalism, viewpoints about history, logic and propaganda) in the problem.

Korea and Japan is disputing about a group of small islets in the Sea of Japan (Korea calls "East Sea") that occupied by South Korea since 1954.

I have read both explanations (but most of them are written by Japanese). It's curious. Both people believe there are lots of evidences that support their own conclusions. For example both shows old maps, but interpret differently (of course for the benefit of each of them.)
It seems that if the International Court of Justice judge, Japan could well win. (But my opinion may change depending on the new knowledge.)

BTW I found that there are some misunderstanding or lack of sensitivity between both people (Korean and Japanese). e.g. Some Korean people seem to think that Japanese want to usurp Dokdo in spite of knowing it belong to Korea. But it's not true. As far as I know, Japanese who concern with this problem believe that Takeshima is "logically" Japanese territory and that Korea should accept the "logical" conclusion. I guess Korean believe the exactly equivalent thing (Korea is "logically" right.)
Another example: It seems that Dokdo became the important symbol of independence or unity of Korean nation in their history, but most Japanese people don't concern with the fact.

So far I'm interested in the fact that the argument don't go well between two nations. Curious from my logical point of view.