There was a thread on this a while back. But to answer your question I believe this originated back to when training was done in tandem, open cockpit aircraft. The student sat up front and the instructor sat behind him. It was often very noisy because of the open cockpit so whenever the student was screwing up the instructor yanked on his/her shirt tail. After the student soloed, their shirt tail was cut off to signify that they didn't need their instructor yanking on it anymore.
I'm not 100% positive on this explanation, but it's the one that i've heard the most and the one that makes the most sense.