In the The West Wing episode "Galileo", the President plans to do an event televised to schools nationwide centered around a Mars lander called Galileo V. The lander runs into trouble, disappearing from communication, probably destroyed, and most of the staff assumes the event should therefore be canceled. CJ, the Press Secretary, objects:
We have, at our disposal, a captive audience of schoolchildren. Some of them don't go to the blackboard and raise their hand 'cause they think they're gonna be wrong. I think you should say to these kids, 'you think you get it wrong sometimes, you should come down here and see how the big boys do it'. I think you should tell them you haven't given up hope, and that it may turn up, but in the meantime, you want NASA to put its best people in the room, and you want them to start building Galileo VI. Some of them will laugh, and most of them won't care, but for some, they might honestly see that it's about going to the blackboard and raising your hand.
As I have grown gradually more adult over my lifetime, I have grown more comfortable admitting "I don't know", increasingly cautious of ultracrepidarianism*. Some advisors have suggested I could stand to express more confidence about what I know, but others have agreed with me that it can be a powerful thing to say to students, "I don't know, but let's look it up together!" It's okay not to know; what's really important is wanting to know and the skill of finding out.
*Meaning "beyond the shoe", from a story from Pliny the Elder where the god Apollo paints a painting, and a shoemaker notices he's messed up painting a shoe, so the shoemaker points it out, and Apollo recognizes he did it wrong and repaints the shoe, so the shoemaker comes back the next day and is emboldened by his previous success to point out what he thinks is an error elsewhere in the painting, but that one is not actually an error, so Bad Things happen to the shoemaker because he just criticized a god on a non-error, leading to the admonition, "shoemaker, not beyond the shoe" -- do not opine on matters outside your expertise.