The bonus discovery that the (car (cdr some-cons-cell)) could be shortened to CADR via a macro was just icing on the cake. Now we have a macro that can access any part of an abstract tree. Nice.
There's nothing intuitive about programming. There's no analogy you can apply to CAR and CDR or even CONS which will suddenly make sense to your primitive mind. You can't pick up a cons cell in your handle, fiddle with it, and throw it back at the computer. There's no analog in nature which resembles it. It's an ephemeral thing that only exists inside a machine because an idea someone had made it so. So stop looking.
If that's the biggest hurdle to learning Lisp I'd be surprised if someone could be taught to program in any other language. Try teaching C declaration syntax to someone.
char *(*c[10])(int **p);
I can explain a cons cell in five minutes tell you that there are two functions for accessing its sub-parts and we can move on.... to red-black trees, skip lists, linked lists, circular buffers, trieps, whatever.
Update: I don't mean to say I'd be surprised if someone could be taught to program in any other language in any sort of glib or pejorative sense. Of course one can learn to program without hearing about a cons cell. What I mean by that is it takes some willingness to accept abstract concepts and turn them into symbols in order to learn how to manipulate them.