The time that I was most afraid as a CFI was when I was flying with this guy named Mike. I think that Mike had a learning disability or something because after 10 hours or so, he was nowhere being able to maintain heading and altitude at the same time.
We were landing after one lesson and as we rolled out, all of a sudden he stomped down on the right rudder pedal for absolutely no reason. The airplane almost departed the runway, but I managed to regain control. It would have been highly embarassing to groundloop a C150. Not to mention that my life flashed before my eyes. After that, since I had already put in my notice, I turned him over to the FBO owner.
I also had another situation with an instrument student in which we had a audio panel failure. The intercom worked between me and my student, but unknown to us, we were transmitting on a hot mic on the #2 comm. We figured out what was happening and cut the #2 radio off but we were still transmitting on it (sounds impossible I know, but it happened). We eventually got ATC to find an empty freq for the #2 comm and we used the #1 for the approach and landing.
I checked out a flight instructor at our local airport. He was telling me beforehand all the hours and experience he had accumulated a couple of months earlier. I made the stupid miskate of saying "this should be no problem".
He nearly balled the airplane up trying to land it.
I had two private students do the same thing to me, except it wasn't on purpose. They couldn't understand why they had to slow down to taxi speed before making a turnoff. On two occasions one guy nearly ground looped me twice; it was the one of the scariest moments I've had in a plane. From then on I always had to say "Remember- apply both brake pedals with the same amount of force, slow straight ahead, and then make the turn!" just before every landing. The guy must have also had a learning disability! Fortunetly he left a few months after.
I"m nto a CFI but when I was the student I went into a inadvertant spin on a stall and I freaked. The CFI quickly took control. I evidently had kicked in some rudder by mistake which set it off. Ooops!