An apology is not a suitable occasion for self-congratulation on the part of the perceived offender with regard to his or her honesty or opinions. I apologize for being articulate. A judgment about the offense. When the offender agrees that what he or she did was wrong, saying so is an important part of making amends. The story of George Washington chopping down the cherry tree, though perhaps lacking in historical veracity, has had enduring appeal in United States culture because of its insistence on the honor of acknowledging one's own wrongdoing.
Many world religions emphasize confession.
But status differences, cultural patterns, and advice of legal counsel may present obstacles to formal confirmation of having made mistakes. A statement of regret. Senator D'Amato's two statements each contained those words, but one created more anger and the other may have decreased the tension. But an attitude of contrition and a statement of regret are basic elements of an apology that will build future trust. These details are often an important aspect of an apology.