No, this isn’t “they don’t care how much you know, until they know how much you care”, although I think there is some substance to that, but rather about how to lead people by making them care.
The most effective, long lasting leadership is about getting people to care, not compelling people to obey. Leadership by compulsion is only as enduring as your ability to make those who follow you fear you. But once you’re not there, or your influence over them is diminished, the obedience you’d once created will likewise disappear.
But, if you can help people care about the principles you want them to obey, by appropriately communicating to them the context of those principles, and the natural ramifications to one’s obedience or disobedience to them, then they’ll obey by choice. They’ll obey because they see the whole picture.
Hence, the importance of communicating context. When asked why (yes, even by your kids), “because I said so” is not an acceptable answer, at least at first.
The better, more enduring alternative is to get them to see the whole picture, and see it clearly enough that they care.