Taking the time to apologize dramatically reduces the tension in a situation. In fact, an August 2002 Psychology Today article titled "I'm Sorry" states:

"An apology is crucial to our mental and even physical health. Recent research shows that receiving an apology has a noticeable, positive physical effect on the body. An apology actually affects the bodily functions of the person receiving it -- blood pressure decreases, heart rate slows and breathing becomes steadier."