Is Australia the largest island?
Australia does get widely referred to as an island as well as as a continent - an island-continent sometimes. My understanding is that "continent" in terms of geology refers to the largest land mass of a continental plate and is more a matter of convention - a general agreement - than precise definition. Such definitions have been subject to revision. 

This definition would have come after continental plates and plate tectonics were confirmed and widely accepted; proposed first by Alfred Wegener in 1912, acceptance did not come until the 1950's and 60's. Naming Australia an island predated this definition and still persists in popular usage but using the current definition it is a continent. 

Greenland, being a part of the North American Plate but not it's largest landmass, gets defined as an island and is now considered the world's largest island.