CESSNA 152 INSTRUCTOR; WITH STUDENT; TOOK OFF BY MISTAKE WHEN THEY HAD NOT BELIEVED THAT THEIR TKOF HAD BEEN CANCELED; CAUSING THEM TO CROSS IN FRONT OF ANOTHER ACFT LNDG ON AN INTERSECTING RWY.

Narrative

THE FOLLOWING RWY INCURSION/MISSED ATC COMMAND INCIDENT WAS THE RESULT OF THREE PRIMARY CAUSES. TWO ACFT IN THE LCL AREA WITH SIMILAR CALL SIGNS (OUR ACFT; AND ANOTHER ACFT) MAKING IT DIFFICULT TO KNOW WHOM THE CTLR WAS TALKING TO. MISSED ATC COMMAND WHILE EXPLAINING A TKOF MANEUVER TO A STUDENT PLT. (THE COMMAND WAS HARD TO HEAR AND WE THOUGHT THE CTLR WAS TALKING TO THE OTHER ACFT). THE ATC COMMAND CAME AT AN UNEXPECTED TIME AND PLACE (THE CTLR HAD JUST CLRED US TO TAKE OFF AND WE WERE TAKING OFF WHEN THE CTLR CHANGED HER MIND AND ASKED US TO NOT TAKE OFF AND STAY IN POSITION). THE EVENT HAPPENED AS FOLLOWS: A STUDENT AND MYSELF HAD COMPLETED OUR RUN-UP WHEN WE ASKED FOR AND RECEIVED PERMISSION TO TAKE OFF ON RWY 20R AT DPA (DUPAGE ARPT). AT THIS TIME IT WAS NOTICED THAT ANOTHER ACFT IN THE AREA HAD A SIMILAR CALL SIGN TO OUR CALL SIGN (OURS WAS AND THE OTHER I BELIEVE WAS). WE THEN LINED UP ON THE RWY AND I STARTED TO EXPLAIN WHAT WAS TO HAPPEN NEXT. WHILE I WAS EXPLAINING; THE CTLR CHANGED HER MIND AND ASKED US NOT TO TAKE OFF BUT BECAUSE I WAS TALKING I DID NOT HEAR WHAT THE CTLR WAS SAYING AND I HEARD WHAT I THOUGHT WAS THE OTHER ACFT'S CALL SIGN; SO I DID NOT THINK THE CTLR WAS TALKING TO US. AFTER ALL; FROM OUR POINT OF VIEW SHE HAD JUST CLRED US TO TAKE OFF AND I EXPECTED HER TO SAY SOMETHING TO THE OTHER ACFT. FROM WHAT I UNDERSTAND; THE CTLR HAD ALSO CLRED AN ACFT TO LAND ON A CROSSING RWY AND THE SEPARATION TIME DID NOT WORK OUT (BECAUSE WE TOOK OFF SLOWER THAN THE CTLR WANTED) AND WHEN WE TOOK OFF; WE CROSSED IN FRONT OF THE OTHER ACFT'S LNDG RWY. HOW TO PREVENT IN THE FUTURE: TRY BETTER AT LISTENING TO CTLRS AND KEEP TALKING TO A MINIMUM WHILE IN CTLED AIRSPACE. THIS IS OFTEN A HARD THING TO DO FOR AN INSTRUCTOR (TEACHING AND FLYING AT THE SAME TIME). BE MORE ALERT WHEN ANOTHER ACFT HAS A SIMILAR CALL SIGN.