The phony sorry-to-end-the-argument apology is the exact opposite of what you should be doing when you’re trying to mend a problem. By essentially sweeping the argument under the rug with a half-hearted and over-accentuated "sorry," the problem gets buried in the angriest part of your brain, allowing it to resurface in the most inconvenient of times.
Not taking a breather
"Taking a moment to engage and think through an issue, understand what happened, and determine if you are in fact actually sorry is important. One way to fix this is to fight the impulse. If you feel yourself starting out a heated conversation with something like, 'Look, I'm sorry, but...' maybe take a beat."
Try going outside, walking into another room in the house, or just closing your eyes and counting to 10.
"I'm sorry you feel that way"
Used by clever bastards everywhere, the "I'm sorry you feel that way" apology tricks the other party into thinking you're actually feeling remorse, while slyly attempting to let yourself off the hook. It's passive-aggressive, almost certain to lead to an argument, and insulting to the intelligence of the person you're "apologizing" to.