Apologizing effectively is a fundamental capability necessary for relational maturity. In one of my books Conversing, I list 21 reasons why we struggle to apologize. Here are five of them:

Fear of vulnerability.
Mistrust. What will they do to me? How will they punish me?
Avoidance. Particularly when we don’t like the manner in which they raised their issue.
Being hard on yourself. You feel that apology is not enough. You would rather find other ways to punish yourself.
Hoping it will just go away. “If I bring it up and apologize I might remind them of something they had forgotten.”

I have seen great results when couples and corporate teams use the following six step biblical approach to apology using the acronym AIRRRR.

Admission of guilt/Confession: “This is what I did"
Impact: "This is the impact I think it had on you.”
Remorse: “I am sorry. I regret what I did. I wish I had not done it. I never want to do this again.”
Restitution: “This is what I am going to do in an attempt to make up for it.” “This is my action plan to hopefully regain your trust in this area.” Remember, you can’t talk your way out of something that you behaved your way into.
Reconciliation: “Will you please forgive me for this? I can’t demand your forgiveness but I would like this relationship to be restored."
Request: In the process it’s also good to end with a request for some kind of support. It could sound something like this: “This has been an area of weakness for a long time; please pray for me that I will overcome it.” "As I endeavour to work on this, please hold me accountable by asking me about it from time to time.”

Therefore confess your sins to each other and pray for each other so that you may be healed. James 5:16 (NIV)