I'm often asked "what is my most interesting teaching experience?" Well....
For me, the most interesting student interaction I've experienced was in my early career. I was in the middle of a Thursday morning lecture/discussion when a student started to get up to leave the class.
The student behind her asked, "Are you okay?"
She replied, nonchalantly, "Oh...my water broke."
Needless to say, I was dumbstruck. I do not remember the grad school class that provided any sort of discussion of what to do when a student goes into labor. Do I get some hot water? Towels? Calipers? Somehow, instinct kicked in, and I walked her to the dean's office where an ambulance was called to take her to the hospital.
I managed to amble back to class and finish, half-heartedly, the day's discussion. More surprisingly, the student was back in class Monday morning ready to dig into learning yet again.