Instructor with trainee reported a rejected takeoff and a critical ground conflict at a non towered airport. The instructor states after repeated departure broadcasts regarding runway in use; departure intentions; etc.; an aircraft appeared opposite direction; 100 feet above and continued along the runway direction and out of the traffic pattern.

Narrative

During a night cross-country flight with a student; we took off from ZZZ1 Airport at XA:00 and landed at ZZZ around XB:00 on Runway XXL entering left downwind at a 45-degree angle. Two other aircraft were in the traffic pattern. After landing; we taxied back to Runway XXL for an eastbound departure. The CTAF was very active; and everyone was in constant and orderly communication.As another aircraft cleared the runway; we announced our takeoff and proceeded to enter the runway; setting the power to full. At that moment; an Aircraft Y announced final for Runway XR; which was the same runway but in the opposite direction. This aircraft had previously announced its position three miles out; and on the CTAF we informed them of the active runway and their incorrect position. When Aircraft Y announced its new position on short final for Runway XR; we were near rotation speed.Upon hearing the announcement of Aircraft Y approaching in the opposite direction; I took flight controls from my student; aggressively and quickly aborted the takeoff; and then cleared the runway as quicker I could. Aircraft Y was less than 100 feet above ground level on final for Runway XR; when we saw the lights and abort take off. After clearing the runway; I reported through CTAF that I had aborted the takeoff and explained the reason for the abort to alert other pilots about Aircraft Y approaching to land in the opposite direction.The aircraft in the opposite direction approached the runway; initiated the flare; but upon hearing my communication; executed a go-around and proceeded east.