Well, as a parent...no. Sometimes you have every intention to do X in Y conditions and timeframe, bit things don't shake out that way.
As a parent, I have words that Eric's grandmother shouldn't hear. I shall try to put them aside and answer calmly.
Would you accept from your child: "No, I didn't do my chores. I intended to, but Bobby had a cool new game and it didn't shake out to leave me time to do them."
Because if you wouldn't, then you definitely shouldn't pull the same on your own child.
You own up to it, instead of teaching them a double standard. That the person with the authority can do things they shouldn't question, but they can't.
Try instead:
"You're right, I did promise to take you to the store so you could get the next book with your birthday money, but my D&D game ran late and the store will be closed before we get there. I'm sorry about that. Can we do it tomorrow instead?"
Acknowledged that you said something and then didn't come through, apologized for, and a rectification suggested.
By all means, let's keep bringing it up and not let the idea be forgotten, but "falsehood" is a bit strong.
True/false is a boolean. "This isn't true, but don't describe it using the word falsehood" is meaningless for something boolean. And a "I will do this by the end of the year", if it is not done by the end of the year is a falsehood. That word is merely descriptive, not too strong.
Now, to undermine a lot of what I'm saying:
I understand from other posters they have it in their Community Update, which is something I didn't know when I posted originally. From my perspective it was promised, with a date they gave themselves so it should be achievable, and then I heard nothing. This Community Update is much better than I originally thought - they are effectively saying "I have not forgotten about this, it's still on my list". That's decent. The original promise is still a falsehood if not done by year end, but this is much more like owning up and having a rectification.