SnowWriter I commend you for asking for information and support on a difficult issue. Here are are some things I've thought about and learned, relative to my students being injured. Some of them are elementary (but I mean no condescension in including them) while others have been hard won by experience transferred as well from my summer profession as an outdoor educator:
As an instructor, I'm a risk manager first in a sport full of internal and external variables. I can't eliminate risk but strive to minimize it in conscious partnership with my students as well as those I work for and with. (The fascinating subject of "actual vs. perceived risk" with all it implicates for "edgework" by my students as I coach them I leave for another thread.)
While many accidents seem to occur "out of the blue" or due to some deficiency on the part of my students, many often are the result of a chain of decisions (mine and others) around these variables in which multiple factors contribute to an injury. The fact that my students may be unfit, unprepared or unskilled is a given (it's why they're here!), necessitating inclusion of this as a variable I assess and manage. My state of mind, physical conditioning, energy and endurance level, etc. also affects my decision-making in my alpine classroom.
While training and experience can serve to minimize injuries, these don't always help. An interesting effect can occur called "risk homeostasis" in which more time on the hill may mean the development of overconfidence which can lead to flawed assessment and decision-making. Sometimes certification or promotion, if it occurs quickly in a career without enough teaching mileage, can have this effect as well.
The capacity to diligently assess risk, manage it and introspect afterwards (no matter how painful that introspection might be) is essential. So is assuming responsibility where it's due, as well as understanding what's beyond my control. And finally, listening to intuition, even if it doesn't seem supported by fact, is well worth cultivating, along with consciously assessing and minimizing my own ego needs as well as the pressures I may perceive from the culture I'm working in.
In my years as an outdoor educator, I've seen a fair number of people leave as well as be counselled out of the field because this burden is too great.
Blah, blah, blah. What does this all mean if a student in your class just tore their ACL, or worse? It feels terrible and of course you feel terrible. I empathize with you. We're not perfect beings. It's like a loss of innocence even if with all your introspection you find you've had no part. Like nolo, I can count on one hand the injuries to my students in my years of teaching. While no injuries were major and all are skiing again I still remember each one, and it's painful to do so. I hold these memories along with the lessons learned very closely. I don't get past them, but I've accepted and learned from them.
In exchange for the opportunity to pursue this wonderful profession, we're ongoing students of risk management. At any given time in our careers we should strive to know what we know, and know what we don't.