Instructor pilot reported an near midair collision in the pattern at ZZZ airport.

Attributes
ACN	1640487
Time
Date	201904
Local Time Of Day	1201-1800
Place
Locale Reference	ZZZ.Tower
State Reference	US
Environment
Flight Conditions	VMC
Light	Daylight
Aircraft 1
Make Model Name	Skyhawk 172/Cutlass 172
Operating Under FAR Part	Part 91
Flight Phase	Final Approach
Route In Use	None
Flight Plan	None
Aircraft 2
Flight Phase	Initial Approach
Person 1
Function	Instructor Pilot Not Flying
Qualification	Flight Crew Commercial Flight Crew Flight Instructor
Experience	Flight Crew Last 90 Days 150 Flight Crew Total 1400 Flight Crew Type 1050
Events
Anomaly	ATC Issue All Types Conflict NMAC Deviation - Procedural Published Material / Policy
Miss Distance	Horizontal 500 Vertical 0

Narrative:

[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.

Original NASA ASRS Text

Title: Instructor pilot reported an NMAC in the pattern at ZZZ airport.

Narrative: [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.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.