C172 INSTRUCTOR AND STUDENT HAVE AN AIRBORNE CONFLICT AT LOU.

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WHEN WE WERE ON FINAL WE HEARD THE DIAMOND CALL IN FROM 12 MI ISLAND AND KNEW THAT HE WOULD BE A FACTOR NEARING DOWNWIND. WE WERE CLBING OUT FROM OUR 7TH NORMAL TOUCH AND GO OF THE DAY. WE HAD BEEN ISSUED L TFC. AFTER THE TOUCH AND GO WE STARTED A NORMAL CLBOUT AT VY AND AT A NORMAL DISTANCE MADE A L TURN TO XWIND. AS THE CLB CONTINUED WE SAW THE DIAMOND COME INTO VIEW. AT THIS TIME I BECAME EXTREMELY ALERT BECAUSE THE CLOSURE RATE SEEMED QUITE HIGH; TELLING ME THAT THIS ACFT WAS NOT ON DOWNWIND; BUT STILL ENTERING FOR THE DOWNWIND; BY THIS TIME MY STUDENT WAS ALERTED TO THE SITUATION UNFOLDING IN FRONT OF US. THE TWR WAS TELLING US TO TURN DOWNWIND AND THE DIAMOND TO TURN OUT AND PARALLEL US. AT THIS TIME WE HADN'T STARTED OUR TURN NOR HAD THE OTHER ACFT; AND WHILE THE CTLR WAS STILL ISSUING INSTRUCTIONS TO US AND THE OTHER ACFT; BEFORE EITHER OF US HAD STARTED THEIR ISSUED TURNS; I TOOK CTL FROM MY STUDENT AND BEGAN AN IMMEDIATE R TURN; AND AS SOON AS TWR RELEASED THE FREQ I INFORMED HIM THAT WE WERE ALREADY IN A R 360 DEGS AND WOULD FOLLOW THE DIAMOND. I FELT THAT OUR GND TRACK GOING FROM XWIND TO DOWNWIND; ALONG WITH THE FACT THAT I HADN'T SEEN THE OTHER ACFT TURN OUT; WOULD HAVE PUT MY ACFT; AND MY STUDENT UNNECESSARILY CLOSE TO ANOTHER ACFT WITH SIMILAR APCH SPDS. MEANING WE WOULD BE NEARLY IN FORMATION FLT WITH THE OTHER ACFT. THEREFORE I CHOSE TO ELIMINATE THE CLOSURE RATE WITH A R 360 DEGS. AFTER STARTING THE 360 DEGS TWR IMMEDIATELY CAME ON AND INFORMED ME THAT I 'NEEDED TO LISTEN TO INSTRUCTIONS AND DO AS HE TOLD ME.' HE ALSO WENT ON TO INFORM ME THAT PERFORMING A 360 DEGS WITHOUT ATC APPROVAL CONSTITUTED A VIOLATION OF FAR'S. AT THIS TIME I REMINDED THE CTLR THAT AS PIC I AM AUTH TO DEVIATE FROM ATC INSTRUCTIONS IN ANY SITUATION THAT I DEEM NECESSARY TO ENSURE SAFE OP OF THE ACFT. I INTERPRETED THAT FROM FAR 91.3(B) STATING THAT IN AN INFLT EMER REQUIRING IMMEDIATE ACTION; THE PIC MAY DEVIATE FROM ANY RULE OF THIS PART TO THE EXTENT REQUIRED TO MEET THAT EMER.