Didn't mean to hurt your feeling!

What is wrong with this statement?

Either you meant what you said or you are not able to say what you mean.
1) If you meant what you said then why being apologetic?
2) If you meant what you said and then felt guilty then you must admit it. Do it in an honest manner. Nothing hurts others as much as dishonesty. Nothing takes away from your social image more than dishonesty. People are very well equipped to detect dishonesty.
3) The second point applies also if you exactly meant what you said and you are not feeling guilty, but just trying to be a smart ass.
4) If you are unable to say what you mean then start by avoiding the expression "Didn't mean to hurt your feeling"! It's not going to help you. It's only going to affirm the state of a mutual indignation between you two. Thus, making both of you feel uneasy!

What to do? Make up for it by action and never try to resolve the issue on rational grounds. This are all assuming that you are not a fool to begin with!