I'm constantly obsessing about the best, most important thing I can deliver at the very beginning of the very first meeting of any class. In the past I've basically said that "Abstraction: Familiarity and Use" is the single overarching principle that I'm teaching in all my classes (math or CS), and therefore that should be the introductory lecture, in some sense, in every single class. I think now I might need to get a bit more topically specific for each class.
For the intermediate algebra class that I regularly teach (which is truly an enormous challenge for most of the students I get), I'm considering this very short mission statement: "Can you follow rules? (Can you remember them?)"
(Here's how I might develop this:) When I say that, I don't mean to come off as some kind of control freak. There are both Good and Bad rules in the world. You should take a philosophy course or some kind of ethical training to identify for yourself what rules are Good (and effective, and you should dedicate yourself to following), and what rules are Bad (and you should dedicate yourself to challenging and overthrowing).
But this course is specifically about the skill of, when you're handed a Good rule, do you have the capacity to quickly digest it and remember it and follow it? If you can't do that, then you're not allowed to graduate from college. The purpose is twofold: (1) testing and training in following rules in general, and (2) an introduction to mathematical logic in specific. The first is a requirement before you're expected to be given responsibility in any professional environment. The second gives you a platform to understand principles of mathematics, which are usually the best, most effective, and most powerful rules that we know of.
So, if you can't follow rules, or if you simply can't remember them, it will be frankly impossible to pass a course like this, and you'll get trapped into a cycle of taking this course over and over again without success.
(Honestly, as an aside, I think the primary challenge to students in my intermediate algebra course is simply an incapacity to remember things from day to day. I know now that we can literally end one day with a certain exercise, and have everyone able to do it, and start the very next day with the exact same exercise and have half the classroom unable to do it.)
I conclude, as I've expressed previously before, with a possible epitaph:
I want to foster a sense of justice.
A love of following rules that are good.
A love of destroying rules that are bad.