from AN 2.21:
"Monks, these two are fools. Which two? The one who doesn't see his transgression as a transgression, and the one who doesn't rightfully pardon another who has confessed his transgression. These two are fools.
How about when the person presenting the apology is not doing it sincerely? How to respond skillfully?
There is a difference between the ideas of apology and revelation or confession. When we in the west read in the suttas about some person recognizing his mistake, we should not be thinking he is apologizing. The idea is that by confessing ones understanding that one has made a mistake and that one understands the nature of that mistake one has made the details conscious. Conscious of the error and the corrective measures needed to prevent its repetition, one is then in a position to take those corrective measures. It is the making conscious that is the important thing.
Apology is asking for forgiveness, not necessarily stating that there will be any effort to reform.
In both cases there is the idea that once an error is sincerely confessed, or a wish for forgiveness expressed in an apology and the other person does not acknowledge the confession or forgive the transgressor, the bad kamma of the deed passes over from the one who is confessing or apologizing to the one confessed to or apologized to. It is beyond my scope to comment on the reality of this belief.
In the case of the apology, going by the Christian practice, there is no requirement that the transgressor understand his error, and one is supposed to forgive, '“seventy times seven times” (490) (Matthew 18:22), a number that symbolizes boundlessness. ... '
In the case of the confession the transgressor must express an understanding of the error and corrective measure before it is necessary to acknowledge it. In this case (and we do not have an example in the suttas so this is just me making up what seems to be a logical response), the polite thing to do would be to explain exactly what was needed before the error could be acknowledged. A diplomatic construction of the statement: "You have not understood your error and consequently I am unable to acknowledge it for you." With perhaps an explanation such as made above to point to what is needed to be done by the transgressor in order to turn this exercise into something helpful to the goal, i.e., change of behavior.
Since the distinction between confession and apology is not likely to be known by most persons in the west, a further act of kindness when faced with an apology that looks to be a sincere effort at change for the better would be to explain this distinction and by that give the person an opportunity to change the apology into a confession.
My personal opinion is that a "sincere" apology has two essential components:
Conventionally you'd accept a sincere apology, meaning, "they have said they will not do it again, and I believe that assurance is true, therefore there is nothing to worry about now and in future, so I can forget it happened and/or behave as if it didn't happen or is forgotten".
This kind of transaction is IMO typical of a parent/child relationship (young children's misbehaviour is forgiven by their parents); and having learned that as a child, you might apply it in adult life too.
I assume your saying, "they are not sincere", is the same as saying, "I not believe their apology is truthful/factual". In that case I imagine that Buddhism might have three bits of advice for you:
Beware (i.e. avoid) having a mind of ill-will -- see for example the "parable of the saw", and the first six verses of the Dhammapada.
Consider what several (physical and social) conditions caused the "offence", and whether you or they can do something differently, to change the circumstances, to prevent that reoccurring
Maybe a "skilful" thing to do is to discuss this kind of topic, possibly using the apology as a good occasion to do so.
But again, in my opinion though, it's possible that a mind of ill-will ("you hurt me, you owe me") might be counter-productive, and would only occasion the other person to deny their offence or to assert their right or to defend their ego etc.
In the suttas, transgressions are addressed thus:
AN7.84:1.1: “Mendicants, there are these seven principles for the settlement of any disciplinary issues that might arise. What seven? Removal in the presence of those concerned is applicable. Removal by accurate recollection is applicable. Removal due to recovery from madness is applicable. The acknowledgement of the offense is applicable. The decision of a majority is applicable. A verdict of aggravated misconduct is applicable. Covering over with grass is applicable.
The applicable principle for apology/confession is The acknowledgement of the offense is applicable. What is notable about this phrasing is that only acknowledgement is required. Conviction, sincerity, deference, resentment, anger, etc. are simply not mentioned. When we acknowledge breaking the speed limit, we may or may not believe in the validity of the rule. If we do not believe the validity of the rule, then we are the fools. If we do not accept the acknowledgement of others when they break the rules, then we are the fools.
AN2.21:1.3: One who doesn’t recognize when they’ve made a mistake. And one who doesn’t properly accept the confession of someone who’s made a mistake.
It's therefore critical to be quite clear about what needs to be acknowledged and accepted as a confession. There's a vast difference between "my car was going faster than the speed limit" and "I believe I should obey that speed limit". The former only requires a simple statement, the second leads to foolish arguments. Sincerity can only be known after a long time and mostly reliably only in the context of one's own practice.
AN3.101:2.1: In the same way, a mendicant who is committed to the higher mind has coarse corruptions: bad bodily, verbal, and mental conduct. A sincere, capable mendicant gives these up, gets rid of, eliminates, and obliterates them. When they’ve been given up and eliminated, there are middling corruptions: sensual, malicious, or cruel thoughts. A sincere, capable mendicant gives these up, gets rid of, eliminates, and obliterates them. When they’ve been given up and eliminated, there are fine corruptions: thoughts of family, country, and being looked up to. A sincere, capable mendicant gives these up, gets rid of, eliminates, and obliterates them.
If someone apologizes insincerely, it's because they are attached to a self-image and are afraid that self-image will be harmed if they apologize sincerely. If we allow ourselves to become offended because we sense that the apology is insincere, then we are attached to a self-image, and fear that our self-image will be harmed if we do not receive a sincere apology.
There is nothing we can do about someone else's attachments except to have compassion for them. We can have compassion for our own attachments too, but we also have to option to try and end them.
The best approach, I think, is to take the apology at face value. If we accept the apology as sincere, we remove an ego threat and make it easier for that other person to give a sincere apology in the future.
The first time they apologise, accept they see the error, and that they intend to not repeat it. Conceptualising another's reasons for a first apology is lack of faith.
The second time they apologise for the same thing, they must also apologise for making a false apology the first time, as they made an error if they intentionally repeated the first error. (so long as they accept an apology implying that the error would not be repeated again)
At some point though, the appology becomes meaningless, even insincere, so if you can maintain the relationship with their error, ask them to not create an extra burden for themselves by falsely apologising, and let them figure it out for themselves. If you do not positively affect their intention, no need to beat them up about it, they should be fully aware of their failure themselves.
If the error is too big for the relationship though, or they are heedless, judge by what is beneficial to you and them. The final stop is AN4.111 - the cutting off of relations entirely (one who does not correct their errors is not a good friend), but that should only be done when it is for the benefit of you and the other, or if the decision would hold no impact on them, but be beneficial for you.
