Skyhawk 172/Cutlass 172
Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Flight Instructor; Flight Crew Commercial
Flight Crew Last 90 Days 246; Flight Crew Total 963; Flight Crew Type 590
Communication Breakdown; Confusion
ATC Issue All Types; Conflict Ground Conflict; Less Severe; Deviation / Discrepancy - Procedural Clearance; Ground Incursion Runway
Flight Crew Requested ATC Assistance / Clarification
Human Factors; Procedure
I was performing a closed-pattern training flight with a student pilot at ZZZ. I was in contact with Tower.On the final leg; Tower advised Cleared to Land XXR; land long for X-2 (taxiway). Student pilot correctly read back instruction and landed between the approach end of XXR and taxiway X-3. Upon landing; Tower instructed 'Exit at X-3'; which the student pilot read back correctly. Student pilot applied heavy braking to exit at X-3 as instructed.Aircraft Y was holding short of XXR at X-3; and as our aircraft began exiting on X-3 it became clear that there would not be enough space to exit at X-3. At this time; Tower instructed our aircraft to 'Stop right there'; which we did. Tower instructed Aircraft Z on final for XXR to go around; and instructed us to taxi to X-2 and exit the runway. I read back the instruction; and affirmed that we had been instructed to exit at X-3. Tower controller disagreed and reprimanded student pilot and instructor. In summary; Tower provided incorrect instructions to aircraft which were properly read back followed; causing an aircraft on short final for landing to go-around; and for two aircraft on the ground to become close to each other.
C172 flight instructor reported ATC issued taxi instruction that created a ground conflict.