C172 Flight Instructor reported taking evasive action to avoid traffic which resulted in a NMAC event.

Narrative

In the southwest practice area in Aircraft X; I was doing a commercial mission with a new hire instructor; and we were doing a ground reference maneuver. As we leveled off; we had a traffic alert for Aircraft Y who was on a head on course for us. My student made the appropriate call and turned right; however; Aircraft Y turned left and was just about 100 feet high descending towards us and turning into us. That this point; I took the controls to maneuver very aggressively to get away from him; but he still was turning towards us. I then asked if he had seen us; and he said yes. I had told him that he needed to turn the other way next time because we got probably less than 100ft from each other. His response was 'I'll send you my flight plan the next time I fly so you can avoid me.' This was extremely unprofessional and shows a high level of invulnerability. This instructor is highly dangerous if he is that rude and doesn't seem to care about proper traffic separation and regard for other people's lives.