The reason for this is that the Shetland Islands are very close to the sea, even inland there is only one part on the mainland which is further than 3 miles from the sea. This means that saltwater is very much 'in the air' and the constant onslaught of saltwater does not create a hospitable environment for very young trees.
In addition, Shetland withstands strong winds, often over 100 miles per hour in winter and this again means that only the very strongest trees can survive.
Shetlanders do plant trees and they may grow to significant heights e.g. twenty or so feet, but there are no towering forests. The bonus to there being no trees, is that trees never get in the way of a view!