Opening the book…
The word 'but' quietly deletes everything before it. 'I'm sorry, but you also...' isn't an apology; it's an argument wearing one as a disguise. People can tell the difference instantly. A clean apology is rare enough that it lands with real weight, and it usually costs far less than the pride it takes to give it.
Name what you did and the effect it had, then stop. 'I was short with you, and that wasn't fair.' No context, no defense, no immediately. If there's something to work out, raise it later as its own conversation. I try to sit in the discomfort of the pause instead of rushing to explain myself.
Don't apologize for things that aren't yours to carry. Over-apologizing dilutes the real ones and can quietly hand blame to the wrong person. Save the clean apology for when you actually got it wrong.