Never heard that one before, have you? The more recognized phrase is, “respect your elders”. Obviously, the latter means to treat those who are older than you with honor, if someone is in authority over you, they are due respect. No issues with that.
But it is also OK to encourage one another to treat those who work for you with respect. Younger people, up and coming leaders, those who look up to you – they all need to be honored. In essence, this is a reminder to leaders to remain humble, and to never take advantage of those for whom you are responsible. Too many people at the head of organizations forget that it is the people in supportive roles who are majorly responsible for the success of their organization. Many times, those in supportive roles are the very reason for the success of their leaders.
Never take these people for granted, never disrespect them, never be condescending to them. Hopefully, they are looking to you for leadership and example on how to treat other people. Show by your behavior how you genuinely care about them and for them. They, in turn, will hold you in high regard.
Respect your youngers, without them, you would fail. They are good people and worthy of your respect.