Sometimes you were right and your tone was wrong. Apologize for the tone and keep the point.

Being right and being decent are separate accounts, and tone draws from the second one. A good point delivered with contempt gets remembered entirely as the contempt, which is why people who win that way often cannot work out why nothing changed. Apologizing for how you said it does not retract what you said.

Split the two next time: tell them you were sharp and you are sorry for that, then keep the point. Do not pretend you were also wrong on the facts to smooth things over. People can take both halves when you hand them over separately.