You can be right about the point and still owe an apology for how you said it.

Content and delivery get judged separately, even when they arrive together. Being correct does not cover how it was said, and the other person is entitled to raise the second without conceding the first, which is why an argument can continue after the facts are settled. Refusing to apologise because you were right confuses the two. You can hold your position and still regret your tone.

Apologise for the specific thing you did, not for the point you made, and do it without the word if. Then leave the argument where it was. Most people meet you halfway once the delivery has been dealt with.