I have to admit that after reading that over, I find myself wondering why we teach students C as their first language...
A beginner's course in C will tell you "uninitialized variables are bad", and "don't use pointers after free", but it won't explain the stack frames or heaps that underpin so much of our computing.
I happen to think that having C blow up in your face (and fixing it) is one of the best ways to learn the subtleties of programming.
If you want to do it that way, you've got to take one thing at a time. Colin's idea of starting with assembly language isn't nearly as crazy as it sounds; I know several people who learned that way. Personally, I would start with very simple, linear programs in a high-level language like Python. Let them get a feel for it, and fiddle around. Then gradually start introducing more and more difficult concepts, like if statements, or looping, and how to use these strange new wonders. Later -- much later -- you'll be able to talk about the low-level details exposed by a language like C. If you try it too early, you'll either get head-explosions or blank stares.
(Incidentally, head explosions are preferable. One of the greatest horrors of teaching is that there will always be students who stare at you with looks of blank incomprehension, and it always might be your fault.)
a) It fails to get people interested in low-level things like call stacks and frames. Someone once told me, "My language frees me up to think about the really important things: like solving the problem at hand. I don't have to worry about things like the stack and where my memory is going or coming from." Perfectly valid point maybe, but I didn't learn about these things because I needed to, I did it because I was interested and curious. I think C and it's pointers played a big role in helping me "get interested".
b) People take the _awesome_ things in high-level languages for granted. When I first moved into python from C, functions as first class entities blew me away! Lisp macros were like learning to do magic. People who have only used a high-level language don't give these features the credit they deserve. (Alright, this might just be a pet peeve of mine...)
I think that C _should_ be taught to students, at a slower pace and in more detail than it was taught to us. And if it occasionally blows up in their face, I think they'll be better off for it.
Unfortunately the Assembly scares off a lot of people from looking at the Computer Engineering degree, as does the very minimal breadboard wiring they have to do, since they assume that's all CE students do. It's a tradeoff of getting more people for a degree program vs. starting off low level. Why do you think so many schools teach Java or C# and never touch an assembly? If your school has to justify keeping a program alive, they're going to have to make it more appealing to a larger audience which unfortunately means creating an easier program or first few semesters, and targeting big-industry popular languages so you can keep subtly hinting at potential good jobs on graduation.