PA28 TRAINING FLT MAKING TOUCH AND GO LNDGS. ELECTED TO MAKE FULL STOP TO ALLOW TRAINEE TO CHK HIS AREA CHART FOR FLT TO ANOTHER ARPT. CLRED TO DEPART RWY 9L; THOUGHT OK FOR A SW DEP. C152 IN THE PATTERN CALLED TFC NEARLY HIT HIM. RPTR CHKED WITH TWR AND WAS ADVISED HE HAD BEEN CLRED TO DEPART W ACCOUNT TFC.

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WE WERE ON A ROUTINE TRAINING FLT (MYSELF AND 2 STUDENTS) CONDUCTING TOUCH AND GOES. AFTER ABOUT 30 MINS HAD GONE BY; I DECIDED TO REQUEST A FULL-STOP LNDG WITH TAXI BACK. I WANTED TO GIVE THE STUDENT A CHANCE TO REVIEW HIS SECTIONAL CHART BEFORE DEPARTING FOR ANOTHER ARPT. AFTER CONTACTING GND CTL; WE TAXIED BACK TO RWY 9L. I SWITCHED OVER TO THE TWR FREQ AND ASKED FOR A VFR SWBOUND DEP. THE TWR CTLR WAS EXTREMELY BUSY; SINCE THERE WAS A LOT OF FLT TRAINING ACTIVITY AT THE TIME. NEVERTHELESS WE FINALLY RECEIVED OUR CLRNC FOR TKOF. QUOTE: 'N.... CLRED FOR TKOF RWY 9L; L TURN APPROVED.' WE DEPARTED AND STARTED A L TURN INTO THE DOWNWIND FOR RWY 9L. GIVING MY STUDENT A TKOF CRITIQUE I TUNED OUT THE TWR CONVERSATIONS WHICH IS THE REASON I MISSED AN INSTRUCTION THE TWR GAVE TO AN ACFT IN FRONT OF US ON THE DOWNWIND. IN MY MIND I WAS ALREADY THINKING ABOUT THE FACT THAT OUR SWBOUND TURN WOULD TAKE US DIRECTLY THROUGH THE LOC FOR THE ILS RWY 9L ON WHICH I COULD ALREADY SEE TWO OTHER ACFT. I INSTRUCTED MY STUDENT TO ASK THE CTLR WHEN HE WANTED US TO TURN SW BUT THE FREQ WAS EXTREMELY CONGESTED. THIS IS WHEN WE NOTICED THE ACFT IN FRONT OF US COMMENCING WHAT SEEMED LIKE A VERY TIGHT 360 DEG TURN. WE CONTINUED ON THE DOWNWIND WITH OUR LNDG LIGHTS ON; ANTICIPATING THE OTHER ACFT WOULD WAIT BEFORE TURNING BACK ON THE DOWNWIND UNTIL HE PASSED OUR 9 O'CLOCK. THIS DID NOT OCCUR. HE KEPT TURNING WHICH LED ME TO TAKING THE CTLS FOR AN EVASIVE MANEUVER. SHORTLY AFTER WE REJOINED THE DOWNWIND (EXTENDED) AND STARTED OUR TURN TO THE SW. WE PASSED IN FRONT OF AN ACFT ON THE ILS WITH ABOUT 1 SM HORIZ SEPARATION. THE NEXT THING WE KNEW; THE PLT OF THE C152 ON DOWNWIND RPTED THAT WE 'NEARLY RAN INTO HIM.' THE TWR CTLR (OBVIOUSLY CONFUSED) ACKNOWLEDGED THE XMISSION BUT DID NOT KNOW WHICH ACFT ALMOST RAN INTO THE C152. THAT'S WHEN I GOT ON THE FREQ AND TOLD THE CTLR THAT THE C152 PLT WAS REFERRING TO US AND I REMINDED HIM THAT HE HAD CLRED US TO DEPART SW. HE RESPONDED; 'NEGATIVE; YOU WERE CLRED FOR A WBOUND DEP. NEXT TIME ADVISE ME WHEN YOU CHANGE YOUR MIND.' I CHOSE NOT TO GET INTO AN ARGUMENT WITH THE CTLR OVER THE FREQ AND WE RESUMED OUR FLT. CONTRIBUTING FACTORS TO THIS PROB: 1) BOTH TFC PATTERNS (RWYS 9L; 9R) WERE ALMOST FULL WHICH LED TO FREQ CONGESTION AND A FULL WORKLOAD FOR ATC. 2) ATC SHOULD HAVE BEEN MORE SPECIFIC ABOUT OUR CLRNC. 3) I SHOULD HAVE ASKED ATC TO VERIFY OUR SW CLRNC.