INSTRUCTIONAL FLC TAKES CLRNC FOR TKOF ISSUED TO MD80. TWR MISSES THE INCORRECT READBACK. AN ABORTED TKOF AND A GAR ARE THE RESULT.

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THIS PARTICULAR FLT UP UNTIL THE MOMENT OF 'CONFLICT' WAS UNEVENTFUL. THIS TRAINING FLT BEGAN WITH 1 HR OF GND INSTRUCTION. A NORMAL PREFLT WAS DONE AS WELL AS NORMAL TAXI TO RUN-UP. AS I RECALL; THE RADIO FREQ 121.7 (GND) WAS NOT CONGESTED. MY STUDENT (PRE-PVT) WAS MAKING ALL RADIO CALLS WITH MY SUPERVISION. TAXI FROM RWY 29 RUN-UP ACROSS TXWY V WAS UNEVENTFUL. GND INSTRUCTED MY STUDENT TO CONTACT TWR 120.7 -- HE DID. WHEN HOLDING SHORT OF RWY 29; I RECALL SEVERAL TFC CALLOUTS FOR BOTH RWYS (29 AND 30) -- ONE OF WHICH WAS A PISTON SINGLE (DON'T RECALL WHAT MAKE/MODEL) ON FINAL WHOSE LNDG LIGHT I BELIEVE I SAW BUT COULD NOT MAKE OUT THE ACFT. ANOTHER CALL TOLD US (FROM TWR) THAT WE WOULD HAVE TO HOLD IN POS FOR A 'DEPARTING' OR 'ARRIVING' (NOT SURE) HVY -- 'XYZ WE ARE GOING TO HAVE YOU HOLD SHORT THERE FOR ABOUT 2 MORE MINS FOR....' THE NEXT CALL I REMEMBER WAS A CLRNC (OR WHAT I AND MY STUDENT BELIEVED TO BE A CLRNC) TO TAKE OFF ON RWY 29 -- AND TO EXPEDITE. MY STUDENT CALLED BACK TO TWR 'CESSNA XYZ CLRED FOR TKOF; RWY 29; EXPEDITING.' I THOUGHT THAT TWR WAS GOING TO TRY TO GET US OUT BEFORE THE WAKE TURB PROB; AND BEFORE OUR TFC ON FINAL. MY STUDENT WAS GOING THROUGH NORMAL PROCS BEFORE TKOF LIGHTS (STROBES AND LNDG) CAME ON (XPONDER TO ALT) AND ON CTRLINE (SEVERAL SECONDS LATER); WENT TO ACTIONS -- PWR TO FULL. THEN WE RECEIVED A CALL -- XYZ; UHHH; DISREGARD; A CALL WAS MADE TO THE ACFT ON FINAL TO GO AROUND AND US XYZ TO STOP. WE WERE; ONLY THEN; TOLD THAT THE CLRNC WE ANSWERED WAS MEANT TO AN MD80 ON THE PARALLEL. I THOUGHT TWR WAS SUPPOSED TO CORRECT ANY INCORRECT CLRNC READBACKS. IF NOT; WHY NOT?