“I’m trying to learn that your boundaries aren’t punishments against us.” It did not erase Thanksgiving morning, or rebuild years of trust in an afternoon.

But it was the first real apology she had ever given me — the first that required her to set down her own ego to offer it — and I have learned that those are rare enough, from the people who raised us, that when one finally comes, it is worth marking, even when it is far too late, even when it changes nothing about what came before.

I have thought a great deal about why that apology was so rare, and so hard for her, and I think it comes down to what a real apology actually requires, which is almost the opposite of what most people offer under that name.

My family had apologized to me many times over the years, in the technical sense — I’m sorry you feel that way, I’m sorry if that upset you, I’m sorry, but you have to understand. Those are not apologies.