Googling for steepest island in the world leads numerous pages claiming that La Palma is the steepest island in the world. Having recently been there, I am inclined to believe it, but it appears the sources just copy each other, without any citing a reliable source. I can imagine many ways to define steepest island in the world. Is there any reliable source to support this claim, or is it just a touristic claim not very well supported?
Wrote a travel blog post titled The Steepest Island in The World? about it after visiting La Palma. With info from the suggestions here and ran automated calculations against a typographical world map.
The way they define steep is vertical distance traveled versus horizontal distance while crossing the entire island from coast to coast, obviously maximizing the line (route) for steepness. The caldera really helps here. So it is indeed be the steepest island in the world under this criteria, if you discard islands smaller than 10 km wide.