Flight Instructor reported while on final broadcasting their position when another aircraft broadcast they were departing opposite direction to the aircraft resulting in the Flight Instructor taking evasive action to avoid a collision with the departing aircraft.
Synopsis
Flight Instructor reported while on final broadcasting their position when another aircraft broadcast they were departing opposite direction to the aircraft resulting in the Flight Instructor taking evasive action to avoid a collision with the departing aircraft.
Narrative
My learner and I departed ZZZ on a local instrument training flight. I had an IFR flight plan on file with the purpose of getting 'actual' IMC conditions for the learner. The clouds were at BKN040; so I decided to stay VFR and monitor the approach frequency. We departed ZZZ for an approach at ZZZ1. Following the RVAV XX approach at ZZZ1 we executed the missed approach and called ZZZ [TRACON] for flight following. After the published missed; I informed Approach we would proceed to ZZZZZ for the RNAV XX beginning at ZZZZZ. We executed the holding pattern at ZZZZZ and approach switched us to ZZZ UNICOM. While inbound; still outside of the FAF; Aircraft Y was also inbound to the traffic pattern from ZZZ2. They adjusted their pattern and followed us to RWY XX. At this point; two aircraft were taxiing out for departure. One aircraft taxied to RWY XX; and the other taxied to RWY XY.I made position reports such as; 'ZZZ traffic; Aircraft X RNAV RWY XX; 4-mile final runway.'Traffic holding at RWY XY; announced their intentions to depart RWY XY to the south. I informed them we were 2-mile final RWY XX. They re-stated their departure intentions to depart to the south.Thinking they may have gotten confused on our position; I stated you would be taking off right at us. I observed them cross the hold short lines; landing light on and commence departure roll. I restated we were on about 1 1/2 miles final and another aircraft was close behind me also for RWY XX. No response was heard from Aircraft Z. I informed my learner to prepare for a go-around and a turn to the right. After Aircraft Z rotated and started the climbout; THEY TURNED RIGHT AT ME. I transmitted; 'Sir; stop your turn; you're pointed right at me!' My aircraft was fully configured for landing; low to the ground and slowed for landing. I had very little energy available to take evasive actions to avoid a stall/accelerated stall. Aircraft Z passed behind us about .5 NM; same altitude. Aircraft Y also executed evasive action low and slow.I refrained from speaking with the instructor following the flight. I believe I would not have been able to maintain a professional tone.Following the flight; I asked the other aircraft that was holding short of RWY XX if maybe I did something wrong. Also a CFI; he said no. He also thought he was going to see a mid-air collision. I was Aircraft X; the other aircraft was Aircraft Z. Due to limited ADS-B coverage; radar data show after the aircraft passed.I'm also an air traffic controller with over 20 years of experience both terminal (TRACON and tower) and enroute experience. THIS WAS BY FAR THE MOST DANGEROUS EVENT I HAVE BEEN A PART OF.I'm not asking the instructor's certificate be revoked; but I believe he clearly violated CFR 91.13; 91.111; 91.113; non-compliance of AC 90-66C; PHAK (Pilot's Handbook of Aeronautical Knowledge); and the AIM.If the CFI is allowing his learner to see these actions; the learner will believe this is acceptable behavior. The learner may also become a danger to other if he is certified as a private pilot.This isn't about being 'cut-off in the traffic pattern' or 'forced to go-around;' we were planning a missed approach as it was. This is about being reckless and danger in the NAS.
Second reporter narrative
Winds were light/variable. One plane was on left crosswind leg runway XX; we were taking runway XX for departing to the east; for a local training flight.My primary student was flying the plane; and made the announcement before entering the runway. Upon rotation I heard a radio call; an airplane was announcing 2 miles final to runway XY; ZZZ. I radioed back asking him to clarify whether he meant runway XY or XX; and I announced we were taking off from runway XX. He answered runway XY; then I saw the lights of the subject plane. I took control of the plane and made an about 20 degree heading change to the left; that way keeping all planes in my sight. We climbed up to 100 feet MSL and turned to the East. The plane on final announced he is going to do a 360 turn. The other airplane on the pattern to runway XX was already at the downwind leg.
Source: NASA Aviation Safety Reporting System (public domain). Reports are voluntary submissions and are not verified by NASA.