A PA38 INSTRUCTOR AND STUDENT STARTED THEIR TKOF ROLL AFTER BEING CLRED INTO POS TO HOLD. TWR THEN ISSUED A CLRNC TO STOP.

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TWR CLRED US TO 'TAXI INTO POS AND HOLD RWY 29L; CAUTION JETBLAST FROM THE FALCON THAT TOOK OFF AHEAD OF YOU.' MY INST RATED STUDENT TAXIED ON THE RWY AND THEN ADVANCED THE PWR AND BEGAN THE TKOF ROLL. I TOLD HIM THAT WE WERE NOT CLRED FOR TKOF; BUT HE DISAGREED AND SAID WE WERE; AND THAT THEY WOULDN'T HAVE WARNED US OF THE JETBLAST UNLESS WE'D BEEN CLRED FOR TKOF. I THOUGHT I MUST HAVE MISSED THE TKOF CLRNC AND AGREED THAT WE WERE CLRED TO TAKE OFF. 3 SECONDS LATER; THE TWR TOLD US TO STOP. I WASN'T PAYING FULL ATTN TO ATC. I WAS RELYING TOO MUCH ON MY STUDENT. WE WERE CONFUSED BY THE SECOND PART OF THE CLRNC -- THE PART THAT STATED 'CAUTION JETBLAST....' WE USUALLY ONLY HEAR THIS SORT OF WARNING WHEN WE ARE CLRED TO TAKE OFF. SUPPLEMENTAL INFO FROM ACN 547066: IN MY MIND I WAS CLRED FOR TKOF. THE TWR TOLD US TO STOP AND REREAD OUR INSTRUCTIONS. WE STOPPED. I ACKNOWLEDGED HIS INSTRUCTIONS. THE REGIONAL JET WHICH HAD LANDED ON THE PARALLEL RWY MUST HAVE BEEN CLRED TO CROSS OUR RWY. THIS RJ WAS APPROX 5000 FT DOWN THE RWY ON A RWY INTXN BTWN THE 2 RWYS. I WILL MENTALLY DIGEST ATC INSTRUCTIONS PRIOR TO READBACK FROM THIS DATE FORWARD INSTEAD OF SIMPLY REPEATING THEM.