Small Aircraft
Flight Crew Commercial; Flight Crew Flight Instructor; Flight Crew Multiengine; Flight Crew Instrument
Flight Crew Last 90 Days 92.8; Flight Crew Total 1914.5; Flight Crew Type 800
Situational Awareness; Training / Qualification
Conflict Ground Conflict; Critical; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural FAR; Deviation / Discrepancy - Procedural Clearance
Flight Crew Took Evasive Action; Flight Crew Rejected Takeoff
Human Factors
Told to taxi into position and hold; after landing traffic. Aircraft Y was cleared for takeoff on a parallel runway. Aircraft cleared the runway ahead of us. There was an aircraft cleared to cross our runway at the nearest intersection approximately 1;500 ahead. Training pre-solo student and expectation bias; along with my inattentiveness were the causes. We started our takeoff roll; saw the crossing traffic; and stopped approximately 1;000 feet from the Piper Cherokee. Tower told us we were not cleared for takeoff.
GA flight instructor reported a ground conflict after they began their takeoff roll with an aircraft crossing their runway 1;500 feet ahead.