Flight Instructor on training flight with student reported a Rejected Takeoff.

Narrative

On Date two foreign pilots arrived at the flight school where I work as a flight instructor. Both looking for what I thought was an intro flight. While holding short of Runway XXL. The pilot in the left seat tells me he wants to fly the takeoff portion of the flight; to which I say that I would shadow the controls at all times. Once on the runway we proceed as planned. Upon reaching 50 knots (5 knots bellow rotation speed) I noticed a crosswind pushing the airplane to the side of the runway combined with pilot's lack of skill and I decide to take full command of the controls. Because the airplane is in an unstable condition I decide to abort the takeoff and advised the tower controller. As Pilot in Command I decided to finish the flight and headed back to the flight school. On Date at XA:17 the controller asks for the reason to abort the takeoff; to which I responded 'strong crosswind and pilot error'. At no time did I mention there was something wrong with the power plant of the aircraft. It all was a miscommunication.