Flight Instructor with student reported a near miss with an airliner while crossing an arrival corridor. Flight Instructor took evasive action to avoid a collision.

Narrative

We were returning to ZZZ from ZZZ1 on a local instructional flight. While receiving VFR flight following from Fort Myers Approach in Class E airspace; just outside Class C; we were crossing an arrival corridor where approach traffic was being funneled in. Runway 24 was in use at RSW; and we were crossing the extended centerline just outside the Class C boundary; directly in line with arriving traffic. ATC assigned us 2;500 feet. As we leveled off; I observed an airline jet approaching us at 2;000 feet. I was flying a small aircraft. From my perspective; the jet appeared to be climbing toward our altitude. It was rapidly increasing in size in the windscreen. At the same time; our traffic alert system triggered.My student began to panic; and I perceived an immediate risk of collision. I exercised my emergency authority as PIC; applied full power; and initiated a right turn. During the maneuver; we briefly descended approximately 200 feet. The descent was not intentional but occurred while executing the avoidance maneuver under high workload.ATC had not issued a heading or lateral vector--only an altitude. In this scenario; lateral separation would have helped prevent the conflict. I notified ATC immediately after the maneuver. My actions were focused solely on maintaining flight safety and avoiding what I perceived to be an imminent midair threat.