Dear Ratso,
you're the instructor, IMHO you were perhaps the one needing some work on your professionalism! If your student could not hack a radio call on what can be a manic freq sometimes, perhaps you needed to work with him/her first before you set them loose.
I operate out of the GC on a weekly basis, on a schedule with passengers and there is nothing worse than trying to call ground wanting a clearance and some new student is stumbling and stammering his way through the calls, it refelcts badly on yourself and whichever school you're working for. Why not just let the student make the calls in the Training area until he builds up confidence? The silouettes up there in the big shiny thing have got the southern T/A to deal with, Jets on RNAV's PJE ops at Byron and Burleigh to try and co-ordinate as well (Used to be a jump truck driver there) in addition to jets asking for Clearances etc. So if you're student cant get it right and he gets a little upset, IMHO he is entitled to.
Just something else... there is also no AIP standard phraseology for UMMM AHHH UGHHH....CAN YOU DO IT....NO...OK GC RADAR THIS IS UMMMM.... you get my point
Oh and if there are any GC ATC guys reading, LOVE YOUR WORK GENTS
Really the most accomodating freindly and professional bunch of ATCers i have come across in my travels