There has been a lot in the news lately about apology. No, this is not intended to be a political blog.
However, the talk got me to think about the concept of apology. Certainly, something we have all had to consider, and, I would think, from both the giving and receiving sides.
The word apology traces back to the Greek — a formal justification. However, current usage is “an admission of error or discourtesy accompanied by an expression of regret”. The definition of apologize that came online is “express regret for something that one has done wrong.”
So, as we’ve been taught, the first step is to acknowledge that you’ve done something wrong and the next step — usually the more difficult — is to express regret for having done it. 
At various times, depending on the unique circumstances, we get hung up on each of the elements of an apology. Tough to acknowledge that we’ve done something wrong and hard to communicate regret. Oftentimes, the elements get confused and one masks the real obstacle to an apology and moving on.
Accepting an apology? Now that’s another blog.