I heard a quote today that summarized the reason most of us are terrible at apologies. It went something like "acknowledging impact rather than defending intent." Think about that for a minute. How many of us have been in the position of defending intent when we're trying to deliver an apology? It may sound something like, "I'm sorry I yelled at you; I've been so stressed out." The person you just yelled at doesn't care about your stress. At least not immediately after getting yelled at. They care about being yelling at and the impact on them. Imagine if the same person said, "I'm sorry I yelled at you; that must have been really upsetting." That leaves room for a conversation rather than a defense.
This is so common in relationships it's often hard to see. Couples try to be understood without realizing how their behavior has impacted their partner. It can be very disarming when someone recognizes their part and takes accountability because it's vulnerable. Give it a try. I bet it takes the steam out of any argument.