I never say I am sorry!
If I have wronged a person, I humbly ask for forgiveness. It is the only way to reconcile wrongs.
Of course you also must do your best to overcome the mistake.
If someone tells me they are sorry.... I am thinking why are you sorry? You seem ok to me? Or I am thinking "yea you are very sorry person".
I always have some call center person telling me they are sorry for what the company they represent has done. I ask them "what have you done to me?" Think about it!
To say you are sorry does not end the wrong. And to say you are sorry is not showing humility.
To ask for forgiveness is to humble yourself, then place the burden on the other person to forgive. Then the issue can be put to rest. With the wrong put in the sea of forgetfulness.
Good points my friend, people sometimes utter the words "I'm sorry" but deep inside they are not and are not willing to ask for forgiveness. although for those who are serious in saying I'm sorry I still can see humility there...