Your integrity, like that of a ship, has a wholeness to it. If you are dishonest, then your “ship” has a hole in the keel and is taking on water. Your integrity is no longer intact, and while a ship can take on some water and still float it is a practice in futility to continually compromise the integrity of the ship that is keeping you afloat.
Admitting when you are wrong not only gives your children permission to be wrong themselves, but it also teaches them how to be honest when they are!