A leader who apologizes to their team first teaches everybody that grace is allowed there.

An apology from whoever is in charge changes what the whole group believes is permitted. Until that happens, everybody assumes mistakes must be hidden, because nobody has demonstrated otherwise. One person with authority saying plainly that they got it wrong rewrites the rule for everyone beneath them. It costs them very little and buys the room something they could not otherwise have.

If you lead anything this week, a team, a shift, a group of younger kids, go first. Name your own error out loud, without softening it, and watch what other people start admitting afterwards.