A Flight Instructor reported they taxied on to the runway to depart from a non-towered airport when they observed an aircraft on an opposite direction final same runway. They made visual contact with the aircraft and it discontinued its approach.

Narrative

I was sitting in the passenger seat of a 2 place aircraft; with the pilot in command and owner of the aircraft at 4N1 at the hold short line for runway 24. We were going to conduct a flight for evaluation purposes. After evaluating the non-standard ASOS and observing several windsocks at the facility; the winds favoring runway 24; with runway 06 and 24 available; the PIC elected to taxi to Runway 24 which was the favorable runway at the time. After completing pre takeoff procedures and observing traffic in the area by visually scanning the pattern; we were set to takeoff on runway 24. I made the radio calls for the pilot flying to provide workload relief. I made a standard call to announce taking the runway while observing an aircraft entering the pattern towards the midfield from the northwest for runway 6. I made several calls about us taking runway 24 which went unanswered.Once our aircraft was lined up ready for take off; the other aircraft flew a base and final for runway 6 and made an announcement that I heard. No other announcements were heard by me or the pilot flying. I immediately answered that we were lined up on runway 24 and if they were observing us from his position. I then asked the pilot flying to get ready to exit the runway as I believed the other aircraft did not hear or see us on the runway. The aircraft replied that they were final for 6 going around. I then observed the aircraft making what appeared to be a base to final turn for runway 6 then proceeded to gain altitude and fly north east. The aircraft which appeared to be Aircraft Y. I asked if they heard any of my announcements to which they didn't reply initially; then replied that they heard me. They asked that we extend our departure leg to make room for him to re enter the pattern to which I replied in the affirmative and the pilot flying proceeded to depart without further incident.