INSTRUCTOR PLT MISINTERPS CLRNC INSTRUCTIONS AND FLIES TO S BOUNDARY INSTEAD OF N BOUNDARY OF SEA ARPT TO CROSS OVER RWYS. HE SEES HIS ERROR AND IS TURNING TO CORRECT WHEN ATC ISSUES NEW CLRNC.

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I WAS ON A VFR TRAINING FLT WITH A STUDENT FROM RNT TO TIW VIA THE VFR TRANSITION WBOUND ACROSS SEA. THE TFC FLOW WAS TO THE S AT BOTH RNT AND SEA AND OUR CLRNC WAS 'CLRED TO ENTER THE SEA CLASS B AIRSPACE AT OR BELOW 2000 FT; CROSS AT THE N FIELD BOUNDARY.' I WAS HANDLING COMS AND READ BACK THE CLRNC; AND HERE I'M NOT SURE WHAT HAPPENED. I THINK I READ IT BACK INCLUDING; 'S FIELD BOUNDARY;' AND IF I DID; I CAN'T IMAGINE WHY; BUT THIS IS WHERE I DIRECTED MY STUDENT TO CROSS; IE; AT 1500 FT ACROSS THE NUMBERS OF RWY 34R. WE FLEW SE THEN LINED UP ON A 250 DEG HDG TO CROSS SEA. ABOUT 1 - 1 1/4 MI FROM THE RWY; I SAW A B737 DEPARTING RWY 16R AND IMMEDIATELY TURNED NBOUND TO CROSS AT THE N FIELD BOUNDARY. ABEAM MIDFIELD; SEA TWR CLRED US TO CROSS MIDFIELD WITH NO FURTHER COMMENT. I DON'T KNOW HOW I MADE THIS MISTAKE. THE TFC FLOW WAS TO THE S; MY STUDENT QUESTIONED MY DIRECTIONS (I ASSURED HIM WE'D BEEN CLRED FOR THE S FIELD BOUNDARY); AND WHEN WE DEPARTED RNT WE WERE GIVEN AN EARLY FREQ CHANGE TO SEA WHICH WOULD EXPEDITE XING AT THE N FIELD BOUNDARY. ALL I CAN THINK OF IS THAT I MISHEARD THE CTLR BECAUSE MY ATTN WAS ON THE STUDENT; AND THERE WAS A LULL IN ARRS AND DEPS AT SEA; IE; NO VISUAL CUES. I AM ABSOLUTELY MORTIFIED THAT THIS HAPPENED! (AND DAMNED LUCKY THIS IS A STATE OF MIND AND NOT A PHYSICAL ONE.)