What happened
The FAA’s narrative, in sentence case. The FAA writes it in capitals and removes private details.
(-23) During taxi out, CFI noticed nose landing gear green light was out. She attempted to swap lights to verify the condition of the nose light however could not remove the light from the panel. Student had accomplished the engine runup and was beginning the take off run. CFI stated that she assumed it was an indication problem as the nose gear held during the taxi and decided to continue with the instructional flight. Shortly after takeoff, at about 500 feet AGL, the cabin door popped open and the CFI decided to immediately return for landing as the airplane was not holding altitude. CFI selected gear down, again no nose gear green light but didn't have time to trouble shoot at this point. Upon touchdown, nose gear collapsed.
As the FAA filed it
(-23) DURING TAXI OUT, CFI NOTICED NOSE LANDING GEAR GREEN LIGHT WAS OUT. SHE ATTEMPTED TO SWAP LIGHTS TO VERIFY THE CONDITION OF THE NOSE LIGHT HOWEVER COULD NOT REMOVE THE LIGHT FROM THE PANEL. STUDENT HAD ACCOMPLISHED THE ENGINE RUNUP AND WAS BEGINNING THE TAKE OFF RUN. CFI STATED THAT SHE ASSUMED IT WAS AN INDICATION PROBLEM AS THE NOSE GEAR HELD DURING THE TAXI AND DECIDED TO CONTINUE WITH THE INSTRUCTIONAL FLIGHT. SHORTLY AFTER TAKEOFF, AT ABOUT 500 FEET AGL, THE CABIN DOOR POPPED OPEN AND THE CFI DECIDED TO IMMEDIATELY RETURN FOR LANDING AS THE AIRPLANE WAS NOT HOLDING ALTITUDE. CFI SELECTED GEAR DOWN, AGAIN NO NOSE GEAR GREEN LIGHT BUT DIDN'T HAVE TIME TO TROUBLE SHOOT AT THIS POINT. UPON TOUCHDOWN, NOSE GEAR COLLAPSED.