This isn't about not holding myself accountable for my actions; it's about no longer reflexively blurting out an apology I don't really owe. It's about changing my default setting from unnecessary guilt.
Refusing to say, "I'm sorry, I was wrong" leaves you powerless because you can't change anything. It alienates you from other people and keeps you trapped inside the conflict forever. But when you say, "I'm sorry, I was wrong," you give yourself the power to change.