“I’m sorry I hurt you” and “I’m sorry you’re hurt” are miles apart.

One version names you as the cause; the other treats the pain as weather that rolled in. Sympathy for somebody’s bad feeling is a kind thing to offer a stranger, but when you are the one who did it, that phrasing quietly moves the problem onto them and their reaction. People hear the difference instantly, even when they could not explain it.

Check which one you are reaching for the next time you have to say it. If you did it, use the version with you in it and no softening clause. Then stop, because every but after that undoes the sentence.