Three words that sometimes fix more than “I’m sorry”: “You were right.”
GRATITUDE
GRATITUDE
Sorry addresses how somebody feels. Conceding the point addresses what they said, and plenty of apologies are offered precisely to avoid that second thing, which is why they can feel thin to receive. The hurt gets acknowledged while the disagreement quietly stays open. Admitting somebody was correct costs more because it changes the record rather than just the mood, and that is exactly why it lands.
Think of an argument where you have since realised they had it right, even a small one, and go say so plainly. No rider, no account of why you thought otherwise. See what it does to your next conversation with them.
Who has been waiting for you to admit they were right?
Free, with nothing to buy inside it.