Flight Instructor reported the failure and separation of an engine cowl while conducting training; resulting in a diversion to the nearest suitable airport.

Narrative

I was doing a training flight with my instrument student knocking out some cross-country time and simulated instrument. On our final leg home from ZZZ1 to ZZZ2 we were cruised out at 3500MSL at about 118TAS and 130ish GS. We had everything set up for our final approach for the day and were cruised out to get home the the last airport. We were on VFR flight following and talking to Departure. My student was at the controls and I was PM (Pilot Monitoring). We were having a discussion about VORs so I looked down at my IPAD to find the nearest one to teach him a few things on the way since we had some free time. As I was looking down he called out bird strike; I immediately took controls and called it out to ATC. I asked for vectors to the nearest airport and ATC gave me a heading to fly. The front right cowling on the plane had ripped completely off and went up and over the plane. Fortunately it did not hit the tail. They asked if I wanted to declare an emergency but I declined for the time being as I still had positive aircraft control. They gave me weather and vectors for ZZZ. They also gave me a phone number to copy as well but stated they just wanted to know that we made it safely to the ground as we had to switch to CTAF. We called on the ground and assessed the damage. After looking at the damage it was not a bird strike it was just the cowling that ripped off. I reported bird strike because that was what my student called out and my head was down for the first loud noise. I watch the cowling rip off and go up and over took about 3 seconds. The plane is safe on the ground and both me and my student are okay.