Definition
Admitting mistakes is the practice of saying — quickly, plainly, and without disclaimers — that you were wrong when you were. Carnegie's principle is "if you are wrong, admit it quickly and emphatically." The emphasis matters: a grudging, hedged admission is read as further evasion; a clean, prompt one is read as integrity.
The distinction from self-flagellation or excessive apology is that admitting a mistake names the specific error and ends. It does not extend into character commentary ("I am such an idiot"), and it does not preemptively offer atonement before the cost is known. The frame is informational, not theatrical.
Why it matters
How it works
A clean admission has four elements. What — name the specific error in concrete terms. Impact — acknowledge what the error cost, to whom. Cause — say briefly what produced the error (without excuse-making). Next — state what you will do differently or to repair it. That structure resolves the issue faster than any defensive posture, because there is nothing left for the other party to push against.
What sabotages admissions is the urge to qualify. "I am sorry, but..." "It was a mistake, however..." Every qualifier reads as a retraction. The admission either stands clean or it does not stand at all.