An apology informed is good; an apology performed is better.
Apology may be scorned, but it retains its inherent value.
Accepting the apology signals the acknowledgment of a need to move forward, but not necessarily together.
When we apologize we end our struggle with history.
"I would like to apologize" may sound like an apology, but it is no more an actual apology than saying "I would like to lose weight" makes you suddenly slimmer.
You can't talk your way out of a situation you acted you way into.