Skyhawk 172/Cutlass 172
Flight Crew Flight Instructor; Flight Crew Commercial
Flight Crew Last 90 Days 150; Flight Crew Total 1400; Flight Crew Type 1050
Situational Awareness; Communication Breakdown
ATC Issue All Types; Conflict NMAC; Deviation / Discrepancy - Procedural Published Material / Policy
Air Traffic Control Issued New Clearance; Flight Crew Executed Go Around / Missed Approach; Flight Crew Took Evasive Action
Procedure; Human Factors
[We] were on final for 27L already having received clearance for a touch and go. Tower suddenly instructed [us] to make a right 360 turn for spacing. With little time to react and the possibility of an aircraft ahead on a short approach; the IP (Instructor Pilot) decided to carry out the instruction. The aircraft was low to the ground; slow and crossed the final for 27R during the turn; flying towards an oncoming aircraft. The IP called tower to check on the situation and it was obvious that the initial instruction had been given to the wrong aircraft. A third aircraft was then spotted turning base for 27L and were then told by Tower to go-around. [We] completed the turn and were cleared to land 27L.The IP debriefed the student after the flight and discussed the tower's instruction and how the IP could have avoided the situation so that the same mistakes aren't made in the future.
Instructor pilot reported an NMAC in the pattern at ZZZ airport.