Instructors at Pacific Skies Aviation proudly carry on the tradition of cutting off a recently-soloed pilot's shirttails!
In American aviation lore, the traditional removal of a new pilot's shirt tail is a sign of the instructor's new confidence in his student after successful completion of the 1st solo flight. In the days of tandem trainers, the student sat in the front seat, with the instructor behind. As there were often no radios in these early days of aviation, the instructor would tug on the student pilot's shirttail to get his attention, and then yell in his ear. A successful first solo flight is an indication that the student can fly without the instructor ("instructor-less" flight). Hence, there is no longer a need for the shirt tail, and it is cut off by the (often) proud instructor, and sometimes displayed as a trophy.
Source: Marchado, Rod, "First Solo Flight", Microsoft Flight Simulator X