While an apology is usually a welcome thing when you're upset, sometimes it's not enough to resolve your angry feelings. If you're still mad after an apology, you may be wondering if you should accept it or not. In this tricky situation, it's important to process how you feel and figure out whether the apology you've received is an apology you can accept.
Give It Time
It takes time for anger to cool down. Sometimes, an apology that seems insufficient right now will look different to you once you've let some time pass. Even if you know intellectually that the other person is saying and doing what he needs to in order to be responsible for his actions, feel free to tell him that you need some time for the anger to pass. If necessary, get some physical distance and avoid speaking in order to give your anger time to burn out without any more hurtful things being said.
Acknowledge the other party's apology by thanking them for it. This gesture of respect and recognition will help any later reconciliation go smoothly. Let her know, however, that you're not ready to accept an apology yet and need more time to think about how you feel and about what you do need in order to move forward. Be firm, even if she tries to push for you to accept the apology now or make arguments as to why you should.
When It's Not Enough
Sometimes, an apology just doesn't cut it. Some hurts and slights can be so deep that it takes more than words to make amends. If you've taken some time and the anger doesn't fade, think about how the other person's actions would have to change and what he'll need to do in order to repair the problem and/or prove to you that he's changed his ways. Let him know that you accept his apology, but that there's more that needs to be done in order for him to actually have your trust.
Missing The Point
You might still be mad because the apology you've received misses the point. The other party might be apologizing for the wrong thing or offering a blanket apology without having any idea why you're hurt. Neither of these things address the problem or show sensitivity to your feelings. You may need to explain your perspective and tell her that an apology needs to be specific and address the real source of hurt. This may require a little more time and self-examination on your end to figure out exactly what the hurt is and how to describe it.