A good leader can say “that was my fault” and “that was your fault” with the same calm voice.

The tone is the whole point. A leader who gets dramatic about their own mistakes makes everybody manage their feelings, and one who gets heated about other people’s makes everybody hide them. Keeping the same level voice for both says that fault is just information here, something to be named and then dealt with.

Practice saying it flatly, out loud if you have to, before you need it. Name your own error first the next time there is one to name. Then say the other one the same way, without the edge.