Owning your mistake first takes the weapon out of everyone else’s hands.

Naming it before anybody else does leaves nothing to catch you out with. Most of the fear around admitting something is really fear of being exposed by someone else, and going first removes that possibility completely. It also changes the subject of the conversation, from what happened to what gets done about it now.

Say the plain version early this week: I got that wrong, here is what I am doing about it. No long explanation, no defense wrapped around the outside. People forgive the mistake much faster than they forgive twenty minutes of avoiding it.