I think when you make a mistake in our culture, if you are in authority over someone else, you don't apologize. In many environments, it is viewed as weakness. I know as a teacher, I encouraged students to let me know if I made a mistake grading their work, and I would give them credit for it if I agreed with their evaluation.
It was relatively easy to look at a multiple choice test where I marked an answer incorrect by mistake. It was more difficult to look at an essay & try to explain to a student what was missing in their answer. I tried to include the feedback when I graded the paper, but there were times when I awarded more credit after reviewing it again, and times when I did not.
I made a bad judgment call during my first year of teaching, and for that I did apologize to the students involved as well as my administration. I awarded extra credit for students in any of my classes who dressed up as a historical character for Halloween. I also dressed up, and I gave out extra credit to students if they could name who I was. One year I was Evita, and I wore a blond wig. One year I was a famous nun from Mexican history called Sor Juana Ines de la Cruz, and I wore a nun's habit costume. My first year of teaching, I had a student who dressed up as Hitler. He was punched by another one of my students in the lunch room.
I do take responsibility for the lack of understanding on my part. I did not anticipate that I should have made some historical villains off limits, but I certainly learned my lesson. I did not anticipate that a student would feel so strongly about Hitler that he would take personal offense to the costume. I find him as abhorrent as many other brutal dictators, and it was an honest mistake on my part to be blind to the emotional connection others would have. I apologized to the student who was punched for not anticipating that his costume would be negatively received, and I apologized to the student who punched him because I did not intend to cause him emotional distress. It was ironic that both of them were my students, because the offended student was angry at 'that teacher' who approved the costume. It was me. Epic teacher fail. There wasn't a whole lot I could do to fix that mistake, except offer my sincerest apologies.
As a mother, it is easy to use my authority over my sons to discipline them in a way that may leave them bitter. I do my best to apologize when I make a mistake, yell in anger, or use my words to harshly. I make sure to differentiate between the apology for my own sin and the guilt they still have for theirs. 'Mommy may have been wrong to yell, but you were wrong to disobey and for that you still deserve punishment'. I am thankful for the Biblical teachings that show me I am not without fault, and therefore I should seek forgiveness as well. Despite the cultural appearance of 'weakness' in offering apology, I am grateful to demonstrate my humanity to my sons as I did with my students. I know it was harder to extend the apologies to students, as they did not always forgive me! I am grateful that while my sons are small, we can practice forgiving each other & mending our broken fellowship. I pray it carries into their adult conflict-resolution skills as well!