Flight Crew Instrument; Flight Crew Flight Instructor; Flight Crew Multiengine
Flight Crew Last 90 Days 65; Flight Crew Total 2805; Flight Crew Type 1400
Situational Awareness
ATC Issue All Types; Conflict NMAC
Flight Crew Took Evasive Action
Airport; Human Factors
While on final to [Runway] XXL to full stop landing; both the my student and I became aware of an aircraft in close in and behind us when tower cleared Aircraft Y to land [Runway] XXL and the plane called [Runway] XXL short approach.  At that time; we were probably 1/8 of a mile from the threshold and 150 AGL.  I announced that we were short approach [Runway] XXL.  At that time; Tower told the Aircraft Y to go around side step left.  I witnessed two aircraft shadows of approximately the same size and merging. I called 'MY PLANE' taking the controls and nosing down lower as Aircraft Y went over the top of us; missing by 50-75 estimated.  I queried the Tower whether I was still cleared to land [Runway] XXL.  Tower replied confirmed we were; so I continued the landing on [Runway] XXL and taxied in to the ramp.After securing the aircraft; we saw the CFI and student pilot of Aircraft Y; asking them if they were the Aircraft Y who had told to go around on [Runway] XXL to which they confirmed.  I asked them if they had seen us on short final to which the student pilot said 'No' they had not.A subsequent call to the Tower indicated that it had been a very close near miss.
I was in ZZZ's traffic pattern with my Instructor in the downwind leg of a traffic pattern; ZZZ Tower gave us traffic to follow who turned base and side stepped to the parallel runway; I didn't see any traffic on base or final and confirmed verbally by saying 'base and final are clear' before turning left base for Runway XXL and then about a mile final for Runway XXL. I asked my Instructor if we were cleared to land and right as I finished speaking; another aircraft on final asked Tower about the traffic in front of them. Tower confirmed our positions and told me to go around and side-step left.  After executing a go around; we were extra; extra cautious and made our last landing a full stop.  After speaking with the other pilot of Aircraft X; who we never were able to see; it appears as my low wing aircraft and his high wing aircraft were in each-others blind spots; him being below me in the Aircraft Y. After he had me in sight he reported about a 200 ft. distance between us.
Pilots reported loss of situational awareness caused a Near Mid Air Collision.