Here's the story as I'd heard it way back in my student pilot days.
In the early days of aviation and flight instructing, the airplanes were all tandem seaters and did not have intercoms (or electrical systems for that matter). The instructor would sit in the rear seat and the student would be in the front. If the instructor wanted to get the student's attention or offer critique about something, he'd reach up and yank on the back of the student's shirt who would then turn around and lean back so he could get yelled at.
When the student's skill level was high enough that the instructor didn't have to yell at him anymore, the student would be allowed to solo and would have the back of his shirt cut off. THis would signify that the instructor felt confident enough to take away the only means of communicating with the student.
But as a previous poster said, you'll hear many different versions or explanations.