NMAC WITH PARALLEL RWY DEP OCCURS WHEN C172 TURNS TOWARDS THE NE VICE NW AS CLRED AFTER TKOF.

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FOR TRAINING PURPOSES MY STUDENT WAS EXPLAINING TKOF PROCS TO ME AS IF I WERE A STUDENT PLT WHILE WE WAITED FOR TKOF CLRNC. WHILE MY STUDENT WAS TALKING ABOUT TKOF PROCS; TWR CLRED US FOR TKOF AND SAID TO TURN; WHAT I THOUGHT WAS TO THE R; NE; AFTER DEP. SINCE WE INITIALLY REQUESTED N DEP; I BELIEVED NE WAS ALL THEY COULD GIVE US DUE TO THE ARPT BEING BUSY AT THE TIME. AS THE TWR WAS FINISHING OUR TKOF CLRNC INSTRUCTION; MY STUDENT STOPPED TALKING BECAUSE HE REALIZED TWR WAS TALKING TO HIM. MY STUDENT DID NOT HEAR WHICH DIRECTION OF DEP TWR GAVE HIM; BUT HE DID HEAR THAT HE WAS CLRED FOR TKOF ON RWY XXL. HE REPLIED TO THE TWR WITH; CLRED FOR TKOF RWY XXL. MY STUDENT DID NOT RESPOND WITH WHICH DIRECTION TO TURN AFTER TKOF AND TWR DID NOT ASK IF WE UNDERSTOOD. I WAS STILL THINKING THAT THE TWR SAID WE WERE CLRED TO TURN R TO THE NE. AS WE PROCEEDED TO TKOF; MY STUDENT ASKED ME; WHICH DIRECTION WERE WE CLRED FOR DEP? I REPLIED; WE REQUESTED N INITIALLY; BUT SHE JUST SAID TURN R TO THE NE. AS WE CLBED OFF THE DEP END OF RWY XXL; WE TURNED R TOWARDS THE NE. AS WE WERE TURNING R; TWR INSTRUCTED US TO IMMEDIATELY TURN L TOWARDS THE NW DUE TO DEPARTING LEAR TFC ON THE PARALLEL RWY. WE REPLIED (ACFT CALL SIGN) TURNING L TOWARDS NW DUE TO PARALLEL TFC. THERE WAS A DEPARTING LEARJET TAKING OFF OF THE PARALLEL RWY; BUT NEITHER I NOR MY STUDENT EVER SAW HIM DURING THE ENTIRE INCIDENT. MY STUDENT AND I CONTINUED TO FLY TOWARDS THE NW WHILE MONITORING TWR FOR THE NEXT 4.5 MINS UNTIL WE WERE ABOUT 7 MI NW OF THE FIELD. WE THEN SWITCHED TO THE PRACTICE AREA FREQ AND CONTINUED WITH OUR FLT LESSON. AFTER OUR FLT LESSON AS WE TAXIED BACK TO THE RAMP; GND CTL INSTRUCTED US TO CONTACT TWR ABOUT THE INCIDENT. MY STUDENT AND I SPOKE TO THE TWR AND THEY HAD ALREADY SPOKEN TO THE CHIEF FLT INSTRUCTOR AT THE SCHOOL. WE THEN CALLED THE CHIEF FLT INSTRUCTOR OF THE SCHOOL AND HE HAD ALREADY SPOKEN TO THE LEARJET PLT ON THE TELEPHONE. THE LEAR PLT TOLD MY CHIEF THAT WHEN HE LOOKED UP FROM HIS RADIOS HE WAS FLYING STRAIGHT TOWARDS OUR PLANE AND HAD TO AGGRESSIVELY DIVERT HIS JET TO KEEP FROM A MID-AIR COLLISION. HE SAID THAT HE MISSED OUR CESSNA BY ABOUT 50 FT. THIS INCIDENT HAS BROUGHT UP SEVERAL GOOD POINTS FOR EVERYONE TO LEARN FROM. ALWAYS READ BACK THE ENTIRE INSTRUCTIONS ATC GIVES YOU; INCLUDING WHICH DIRECTION TO DEPART EVEN IF TWR DOES NOT REQUIRE YOU TO VERBALLY ACKNOWLEDGE. IF TWR ASSUMES THAT PLTS UNDERSTAND WHICH DIRECTION TO FLY AFTER TKOF; BUT NO ACKNOWLEDGEMENT IS XMITTED; THERE IS A MUCH HIGHER PROBABILITY OF AN ACCIDENT OCCURRING. WHEN 2 PLTS ARE ON BOARD; IT IS ADVISABLE THAT BOTH PLTS CONFIRM THAT THEY HEARD THE SAME INSTRUCTIONS; ONE PLT HEARING ATC INSTRUCTIONS IS NOT ALWAYS GOOD ENOUGH BECAUSE WE ARE HUMAN AND HUMANS MAKE MISTAKES.