Never underestimate what you teach your child when you apologise!
It demonstrates that you are human, not invincible and that as a parent you make mistakes. It highlights to your child that you are honest and that you believe in the value of honesty.
A child looks lovingly to their parents, implicitly trusting them. They are not interested in whether you are a perfect being. In fact, no one is and therefore is it best to show your child how human you are from time to time. Showing them that we are all working on improving ourselves and this means acknowledging mistakes is an excellent direction to give a child.
When you make a mistake that effects your child, a simple apology lets them know that at times you need to correct yourself and that this is an admirable quality. Sometimes in our anxiousness to show the best face, we can avoid the truth to look consistent and strong. Actually, the child easily senses that they are not given the truth and can get confused and be given the wrong message. That message is about always maintaining a strong face and never letting your guard down.
By modelling this behaviour to your child, you are encouraging them to look in control at all cost and never lose face. It is much better to show them that the human condition means from time to time mistakes will be made and saying sorry is a way of reconciling with another person to set everything right again. It is also teaching them that to be strong is to recognise in yourself your vulnerabilities. Such vulnerabilities are part of the human condition and if as a parent you show that you are comfortable in talking about such vulnerabilities, they actually become strengths.
When apologising be explicit. Explain what behaviour led you to make that mistake.
“I am sorry that I forgot to attend your concert at school. I was so busy at work that I lost a sense of time.”
By showing your child that you were careless takes the sting away from the issue and gives both of you a chance to talk it through. What is also important here is to discuss ways to help you remember next time when the concert will be held.