The dispute arises in part because there are really two types of continents: Those recognized by cultures around the world, and those recognized by geologists. Cultures can define a continent any way they want, while geologists have to use a definition. And geological research in recent years has made defining continental boundaries less simple than it might have once seemed as researchers find evidence of unexpected continental material.
From an amusing NYT Science article entitled “How Many Continents Are There? You May Not Like the Answers." Of course, the obvious Polanyian question is — are geologists not a culture?