DURING ROLLOUT AFTER XWIND LNDG; SMA; PLTED BY STUDENT PLT AND INSTRUCTOR; VEERS OFF RWY ON UPWIND SIDE.

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I TOOK A 15 HR; POST-SOLO STUDENT TO OUR LCL PRACTICE AREA AND COULD SEE HE WAS OBVIOUSLY NERVOUS AND SCARED. THE SURFACE WINDS WERE VARIABLE; BUT IT WAS VERY WARM AND THE PRACTICE AREA WAS MODERATE/MODERATE. WE MADE 1 TURN IN THE PRACTICE AREA AND I ASKED HIM IF HE WANTED TO RETURN FOR LNDG AND TRY AGAIN WHEN IT GETS SMOOTHER. HE READILY AGREED. I THOUGHT IT WOULD BE GOOD TO LET HIM DO THE FLYING AND I WOULD CONTINUE TO COACH HIM THROUGH HIS ANXIETY. WE WERE CLRED TO LAND AND THE XWIND COMPONENT WAS ESTIMATED BY ME AT 5 KTS. I ASSISTED HIM THROUGHOUT THE FLARE AND TOUCHDOWN; ENSURING THE XWIND CORRECTION WAS MAINTAINED. OUR GND SPD WAS APPROX 50 KTS AND THE FIRST TXWY WAS APCHING FAST. MY STUDENT APPARENTLY THOUGHT WE WERE GOING TO TURN OFF ON THIS TXWY. THIS TOTALLY SURPRISED ME. I WAS EXPECTING HIM TO ROLL OUT TO THE NEXT TXWY AS USUAL. HE HAD NEVER SHOWN SUCH BAD JUDGEMENT ABOUT ROLLOUT AS THIS BEFORE. MY STUDENT BEGAN PRESSING ON THE R PEDAL AND THE BRAKE STARTED TO LOCK UP. IT WAS SO NONSENSICAL TO ME FOR THIS ACTION. I BEGAN TO COUNTER R RUDDER WITH L AND SAID; 'LET OFF THE RUDDER; LET OFF; LET OFF!' BY THE TIME HE LET OFF; WE WERE OFF THE SIDE OF THE RWY; ON THE UPWIND SIDE. THE PLANE SLID SIDEWAYS AND I COUNTERED AS BEST I COULD WITH RUDDER. BY THE TIME WE GOT ON THE RWY; THE PLANE'S L GEAR STRUT HAD TOPPLED A RWY EDGE LIGHT OUT. ONCE UNDER CTL AND SAFELY OFF THE RWY; MY STUDENT TURNED TO ME AND SAID 'WHAT HAPPENED?' HIS PERCEPTION WAS THAT I HAD PUSHED THE R RUDDER PEDAL. HE DENIED WANTING TO EXIT ON THE FIRST TXWY.