The Dokdo/Takeshima dispute is essentially a product of the 20th century. Historically, uninhabited islets in East Asia like the Dokdo/Takeshima, the Diaoyu/Senkaku, or the Spratleys were not formally "claimed" in the way that they are today- it is only since the mid-19th century that the idea that these islets should be the exclusive lawful territory of a single nation-state caught on, because the concept was adapted from Western definitions of sovereignty. The status of the island was a moot point during the period where Japan colonized Korea, but since independence in 1945 it is clear that the island must belong to either Japan or South Korea- it can't be both, it can't be neither, and no third country would be acceptable either. But since the islands have historically not had the clear status that populated islands like Jeju or Tsushima had, and there is no long-established population there which a self-determination argument could be based on, there is really very little basis for saying that either has an especially strong claim. And yet, under current rules of sovereignty, it must belong to one of them or the other.