I understand the sentiment. But I disagree. Everyone deserves to be put first at one point or another. This is the kind of toxic rhetoric that lazy admins push on teachers: "Oh we KNOW youll go the extra mile. We know youll do whatever it takes, etc."
Refusing to put yourself first is why so many people burn out. It is possible to treat your employees like they are more important than someone else every now and then. In fact, it helps to prevent burnout.