Why is Greenland an Island and Australia a Continent?

What makes a continent? There's no simple definition, but Simon Whistler of Today I Found Out has some observations about why our geography ended up being labeled the way it is.

(YouTube link)

I never really thought about comparing Australia and Greenland, but both places are pretty much outliers in any category. Greenland is closest to North America, but considers itself part of the European continent, mainly because it's a part of the Danish realm. How the people of a place consider that place has more lasting meaning than some definition that someone elsewhere came up with