In declaring themselves to be "wretched" they were giving a reason for:
a) why they did the thing that caused offense (i.e. I'm a wretched excuse for a human being) or b) why they deserved mercy (I'm wretched and don't deserve mercy but I seek it anyway).
This approach is flawed because debasing ourselves in order to excuse our bad behavior or as a reason we should receive mercy is not consistent with Scripture.
The idea of "giving a reason" or "giving an answer" is encapsulated in the Greek word apologia. You might recognize this word as the root of our modern English "apology" or "apologize". The concept of "apologetics" (defending your faith) also stems from this Greek word.
Paul begins his discourse in Acts 22:1 by saying "hear my defense" using the word apologia.
Instead of "I'm sorry" we sometimes hear people use the expression "I apologize."
In a literal sense saying "I apologize" means "I'm giving an answer/excuse/defense" for what I have done.
I did "x" and it offended you. Here is my excuse for what I did. That excuse should be a satisfactory reason for you to forgive me.
This approach comes with the incorrect assumption that by providing an excuse or a reason (i.e. by defending my actions) I am now worthy or capable of being forgiven.
While the approach is flawed this particular example points us to the crux of the matter: forgiveness.
Please Forgive Me
Peter asks Messiah how often we should forgive sins against us. The Lord answers the question by saying "seventy times seven" (Matthew 18:22). He did not mean 490 times (as if we should keep a running tally of the number of times we have forgiven someone!), he simply meant that we should completely forgive as often as necessary. [Seven being symbolic of fullness or completeness. -ed]
If we sin (through words, actions, or inaction) against another person there is a debt we now owe them as a consequence. It is this debt that Messiah says we should forgive.
And forgive us our debts, as we also have forgiven our debtors. (Matthew 6:12)
Scripture shows us the pattern of the appropriate response in these situations:
Therefore, confess your sins to one another, and pray for one another so that you may be healed. The effective prayer of a righteous man can accomplish much. (James 5:16)
If we confess our sins, He is faithful and righteous to forgive us our sins and to cleanse us from all unrighteousness. (1 John 1:9)
b) Take responsibility
If we say that we have no sin, we are deceiving ourselves and the truth is not in us. (1 John 1:8)
c) Seek forgiveness
For if you forgive others for their transgressions, your heavenly Father will also forgive you. But if you do not forgive others, then your Father will not forgive your transgressions. (Matthew 6:14-15)
My own personal pattern for dealing with my sin and offense against others:
a) address the person by name and confess my action hurt or offended them, b) take responsibility for what I did, c) ask the other person to forgive me.
Instead of saying "I'm sorry" or "I apologize" the following is far more Scriptural and appropriate:
"Jeff, I realize that my words hurt your feelings. I spoke them in anger and I was wrong. Please forgive me for saying that to you and hurting your feelings."
Don't debase yourself and say "I'm sorry." Don't defend yourself and say "I apologize." Do confess your sin and seek forgiveness.
If we approached both G-d and men with genuine humility in dealing with all of our sins in a manner such as this then believers would all be in a better state.
Now to the King eternal, immortal, invisible, the only God, be honor and glory forever and ever. Amen. (1 Tim 1:17)