C172 Flight Instructor reported the engine cowl flap detached during climbout resulting in an immediate return to the departure airport.

Narrative

On Day 0; during a flight instruction lesson the engine cowl flap unlatched short after rotation during the initial climb; As soon as this happened we requested ZZZ Tower to stay in the pattern and return for a full stop. Tower was briefed on the situation and we were shortly given a clearance for a full stop on XXL. We taxied the aircraft back to the schools hangar to asses if there was any damage. Upon inspection we discovered the hinge had been damaged and the cowl was bent in such way that it would not have a tight fit when trying to close. No other damage was sustained to the aircraft but we determined it was unfit to fly. After we parked the make and double checked the aircraft for any other damage; we briefed on what we could have done better. From a pre-flight point of view student could have doubled checked that the cowl flap is properly latched to the engine cowl; and even though student has been taught how to close it before during his pre-flight lesson; we went back to the plane and showed him how to make sure latch is properly secured. We also pointed out were in the pre-flight checklist it discuss to make sure vents; latches; and doors are properly secured. Last thing we discussed on how I the Instructor could have avoided this by not being complacent. I explained to the student how once you start flying every day its easy to get in a 'routine' and assume everything has been done the right way or just simply being 'lazy' and not properly going over simple things that could turn deadly. I think it was a good and valuable teaching experience on how even small little things can have such a big impact on a flight; its also not cheap. We will continue to talk about how to always make things more efficient and safe.