GA Instructor pilot reported a near miss with another aircraft while in a descent on a training flight with a student in visual conditions. The instructor was alerted by ForeFlight automation without a visual sighting; and maneuvered away from the conflict.

Narrative

I was the PIC and flight instructor on a training flight with a student pilot in a Small Aircraft; operating under VFR. While on a southbound heading at approximately 2000 feet MSL; I became aware of another aircraft flying northbound about 400 feet below me (head on). I did not have visual contact; but was notified by ForeFlight/Sentry via iPad. I did not obtain visual contact until after the conflict. Upon seeing this indication; I immediately began a climbing left turn; unaware if the other aircraft was aware. The other aircraft then began a right turn following right-of-way procedures. I reacted quickly and did not consider the right-of-way rules initially and attempted to just get away and above the other aircraft. There was no prior or post contact with the other aircraft via CTAF or any known frequency.As an instructor; I was covering straight and level flight with a student and became too fixated on instructing and momentarily lost situational awareness. Neglecting a constant scan; I put myself and student in a potentially dangerous situation by not prioritizing safety throughout the entirety of our flight. I explained to my student my incorrect response of making a left turn; when we should have followed right-of-way rules. My primary understanding of why this occurred was due to my fixation on instructing and undermining the required situational awareness and safe practice in a local area. Thankfully; me and the other aircraft managed to avoid one another; but moving forward; I need to maintain situational awareness and safety standards throughout flight; and if I find myself in a similar situation; initiate corrective action in accordance with the FAR/AIM.