Your children (and your partner) are the most important people in your life, so the quality of your relationship with them is absolutely vital. They are human, and make mistakes, and when they do, you make them apologize. But you are human too, and they know it, and by saying ‘sorry’ when you are in the wrong, really proves to them that you are.
Saying ‘sorry’ shows your children that you are not infallible and that you make mistakes like them. Your children will love and respect you hugely for saying this simple word to them. After you have said it and the ‘dust has settled’, you will see that it improves the quality of your relationship with them even more.
This is particularly important during their teenage years, when they believe that they are always right, and that you as their Dad, ‘just don’t understand’. It is very hard for you to admit that you were wrong, I know that, it has been for me, but between a father and his children there is no room for misplaced pride.
I would love to hear of your experiences with your children once you have said ‘sorry’ to them about something. I’m sure their reaction was very positive