Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Flight Instructor; Flight Crew Commercial
Flight Crew Last 90 Days 666; Flight Crew Total 599; Flight Crew Type 433
Communication Breakdown; Situational Awareness
ATC Issue All Types; Conflict NMAC; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Air Traffic Control Issued Advisory / Alert; Flight Crew Executed Go Around / Missed Approach; Flight Crew Took Evasive Action
Human Factors
Near miss with a T-38 during a right downwind at ZZZ Runway XX. The T-38 did a go around for Runway XY and started a climb while we were turning crosswind to downwind; upon intersecting Runway XY the T-38 had leveled off co-altitude and was headed at us from the arrival end of Runway XY. IP (Instructor Pilot) had them in sight and was about to take controls to make evasive action when the T-38 aggressively pitched up as if they spotted us as well. Ultimately; the T-38 passed over and behind us within 500 ft. The T-38 was on a military frequency however we overheard Tower respond to their call with something along the lines of 'He was in a right downwind for [Runway] XX; no factor'.
ATC cleared me for right traffic out of Runway XX and I was staying in the pattern. ATC had cleared a T-38 for landing on Runway XY. The T-38 performed a go around and my instructor point out that he was headed directly for us. I saw him aggressively pitch up and climb above our wing.
Flight Instructor and Student reported a Near Mid Air Collision and observed the other aircraft pitched up aggressively to avoid collision.