C172 Flight Instructor reported a loss of aircraft control on landing by the student pilot while doing crosswind training. Student lost directional control on touchdown; resulting in a runway excursion. While attempting to return to the runway pavement; the aircraft's propeller hit one of the runway lights.

Narrative

My student had struggled with crosswind landings so we made a concerted effort to expose him to gusty and crosswind conditions. After practicing in gusty conditions with varying degrees of crosswinds; we went to ZZZ which was a direct crosswind at 10 - 18 kt. After a poor attempt by my student; I demonstrated one to a full stop. To help him with proper crosswind techniques; I had him just do a low approach while demonstrating the side slip technique. He executed the low approach with the side slip down the runway really well so I told him I wanted to land the next one. The approach was stabilized and he had proper correction in. However; after touching down; we started veering off the runway into the upwind side. ZZZ is a very narrow runway so we were quickly partially in the grass.I felt that if I initiated a go-around without having directional control; it would have been more dangerous than going power idle and regaining control. I added left rudder and with power idle; we started getting back on the pavement. However; in the process; our propeller hit one of the runway lights.Looking back; as an instructor I need to do a better job at balancing the needs of my student for training; while also making sure it's a safe environment where mistakes can be made without any repercussions. Taking my student to a narrow runway when he had exhibited struggles previously in similar conditions was poor decision-making on my part and did not allow him to make those mistakes in a safe environment.