Our success as students, parents and professionals relies in part on how well we get along with others. And sometimes, we're going to make someone else angry, maybe even unintentionally. The next time you're the one doing the angering, before you apologize or explain what your intentions were (not the right thing to do) refer to this great article from the Harvard Business Review.
Here's a related past post of mine on how to handle customer complaints. It doesn't matter who's right. If a customer is angry, the first step to resolution isn't to explain away the problem or even to apologize, but to acknowledge how your customer feels.