A Flight Instructor departing a non towered airport reported they taxied onto the runway with another aircraft on short final; which initiated a go around.

Narrative

While departing ZZZ in daytime VFR conditions; our aircraft was holding short of Runway XX for a straight out departure back to ZZZ1 under VFR. Two occupants. While stationary short of XX in a fairly busy pattern; we completed checklists as per normal. While scanning final; base and downwind; as well as using ADSB traffic tools; we agreed we were safe to depart Runway XX straight out. We heard another aircraft extending their left downwind for a 'twin departure' and thanked them. While crossing the bars for XX; myself as Pilot Monitoring/MEI; I heard the words 'going around XX sidestep' and quickly looked up on final once again; and saw a silver single engine aircraft at maybe 500 ft.; within a mile or less final. I grabbed the brakes and we stopped with maybe half our plane over the hold short bars; and apologized. Go around aircraft sidestepped to the right of Runway XX and began a climb out. We waited until the go around aircraft was midfield or further; then we announced lining up and waiting; visually clearing final and bases before pulling out further. We acknowledged the go around aircraft once again; and said we both (myself and student) couldn't see you (silver/grey) against the clouds; and also did not have you on ADSB traffic. Another aircraft in the pattern also said that the go around aircraft was not appearing on their ADSB traffic screen either. Go around aircraft sounded puzzled upon hearing that. Once go around aircraft began a crosswind turn to join left traffic XX; we commenced our takeoff roll on Runway XX; straight out. No further events for the balance of the flight.Suggestion: simple eyes outside scanning and radio usage at a busy untowered airport can never be forgotten. ADSB provides incredible situational awareness; but can sometimes be faulty; or inoperative; as possibly shown by the surprised sounding go around pilot when told his airplane wasn't showing up for another pattern aircraft either. Reinforce to student's checklist usage while stationary; and eyes up while moving/parking brake off. Reinforce usage of landing lights and taxi lights to increase visibility; especially during bright daytime conditions against a white or grey sky/background; as well as double checking proper CTAF frequencies set and active.