C172 Flight Instructor reported a NMAC during takoff with opposite direction traffic that was not communicating. Flight Instructor took evasive action to avoid a collision.

Narrative

ZZZ is operating under class G airspace with overlying class E airspace. The flight constituting this report was a 91 training flight with a clients owned airplane. ZZZ has been NOTAM with AWOS negative wind for several months now and no repair is currently scheduled. The pilots must use wind socks for surface wind reports. At XA10L there were three airplanes working the XX Runway at ZZZ. The pilot involved with the NMAC apparently announced his intention of departing Runway XY to the South. The winds at the time were 330-320 7-10kts based on sock observations. The pilot departing Runway XY was Aircraft Y. The pilot was en-route to ZZZ1. There was no traffic-ADSB noticed anytime the pilot was flying in the valley although the airplane is ADSB equipped but probably with a 978mHz transponder. When our airplane Aircraft X was on the departure roll at 1 there was no indication of a departing aircraft. Right after 1 I picked up the landing light of Aircraft Y. In the next second my student and I had a as briefed successful transfer of controls and I made a dogleg into the 'upwind leg'. At the same time that the diversion happened Aircraft Z was making a departure/take off call on the communication making it unable for me to communicate. As soon as the communication ended keeping the departing Aircraft Y in sight; I notified Aircraft Z. Aircraft Z nor the taildragger behind him all working XX heard a call and they commented on frequency how close it was. I luckily spotted the departing Aircraft Y very soon after rotation and made evasive action not leading to much of an issue. This report and NMAC collision highlights a few risks. 1.ZZZ weather reporting being NOTAM inoperative leading to confusion on proper runway especially if pilots do not observe wind socks. 2. The inadequate function of ADSB transponders with terrain3. The lack of required communication equipment (although the pilot made a departure call verified by FBO employee monitoring with a handheld radio)4. The diligence in requiring eyes outside especially with runways so long with departure end not visible. 5. The importance of pilots to Adhere to proper technique to avoid Mid Air Collision and the importance of Advisory Circular 90-66CThe pilot of Aircraft Y exchanged communications after the fact and all was respectful and there were no hazardous attitudes present. Mistakes happen and we all learn from them. Opposite departures are a common occurrence and pilots accepting tailwinds on departure due to the Obstacle Departure Procedure (ODP) for this airport is to the S and the only approach is landing to the North.