Why do we say "I'm sorry"? Is it out of a feeling of requirement, that we should say it? What does it even mean? "I'm sorry" is a human approach to forgo confession of sins. Thing about the difference between saying "I'm sorry for such and such" as opposed to "I sinned when I (fill in the blank), will you forgive me?" The latter is a true confession of sin against another and requires us to recognize it as just that. I don't know about you, but I have a hard time saying I am sorry, but how much harder would it be to actually call it sin and confess it and ask for forgiveness. Ouch! what a blow to our pride. This is exactly why we have come up with the shortcut of "I'm sorry" and the typical response "It's alright". However, this is not biblical approach to handling problems. God expects much more out of us and we know that from His example. He instructs in the Lord's prayer to confess our sins and ask for forgiveness from Him. This is not just saying "I'm sorry God" as a blanket over all our sins, but rather He expects us to confess our sins by recognizing each sin for what it is. We are also to ask for forgiveness which I will now go into more detail about our failure to forgive the way God wants us to forgive.
Forgiveness is not a feeling. Sometimes we don't feel like forgiving others and so instead we hold a grudge. It is also not adequate to respond to someone's request for forgiveness with "it's alright". Obviously it is not alright or they would not have needed to come confess their sin against you and ask for your forgiveness. A request for forgiveness requires a "yes, I forgive you" or a "no, I won't forgive you" (of course the latter response is not a Christlike response). So then what does it mean to forgive someone? Forgiveness is a promise. When you say "Yes, I forgive you," you are actually saying "I promise that (1) I will not bring this matter up to you again; (2) I will not bring it up to others; and (3) I will not bring it up to myself - dwell on it in my mind." Wow, that is not something to take lightly. This is how God forgives us, "Your sins and iniquities will I remember against you no more" (Jer. 31:34).
Can you imagine how much better our relationships would be if we truly confessed our sins against each other and asked for forgiveness and then if we truly forgive following the example of how God forgives us? As difficult as this may be, I think I'm going to give it a shot, starting with my husband.