Sure, you know how to self-flagellate, but do you know how to apologize? Saying “I’m a stupid idiot” is not the same thing as saying “I did something wrong.”
People who want an apology pretty much never want to hear “I’m a stupid idiot.” If someone is actually trying to get you to say you’re a stupid idiot, it’s not because it will make up for a mistake you made or harm you caused. It’s because they want you to feel like a stupid idiot. People who care about you do not want you to feel like a stupid idiot and it hurts them when they see you putting yourself down in their name.