The whole reason for apologies is emotional: person who was hurt feels a relief knowing that the offender understands their mistake, regrets it and intents to a

The whole reason for apologies is emotional: person who was hurt feels a relief knowing that the offender understands their mistake, regrets it and intents to avoid similar behaviour in future. Offender feels a little better knowing that the victim does not hold a grudge and does not intend any revenge. Of course if neither victim nor offender felt any human emotions then apology would make no sense to them.