The author’s statement, “or declare it false”: this is the reverse case. Someone tells him something, and he says, “You are lying. If what you say is true, then my slaves are free.” His purpose is to declare it false—that is, by this statement he seeks to emphasize that he considers the man to be lying.
The author’s statement, “he may choose between fulfilling it and offering the expiation for an oath”: it is like an oath. That is, just as if you swear concerning something: if you do it, then no expiation is due; but if you do not do it, then you must offer expiation. In short, we say: regarding this vow, if you wish, fulfill what you have vowed; and if you wish, offer the expiation for an oath.
The evidence for this is the hadith related by Sa'id in his Sunan (1): “There is no vow in anger, and its expiation is the expiation for an oath.” As for the reasoning, they said: it carries the meaning of an oath, because by this vow he intended only prevention, inducement, affirmation, or declaring something false. The Prophet ﷺ said: “Actions are but by intentions, and every person shall have only what he intended.” (2)
Let us give an example: a man says, “I owe Allah a vow that, if I do such-and-such, I shall fast for three days,” and then he does it. Is he required to fast for three days, or to offer the expiation for an oath?
The answer is that he has a choice: if he wishes, he fasts for three days; and if he wishes, he offers the expiation for an oath, because this vow has the same ruling as an oath.
If we say that it has the same ruling as an oath, then which is preferable: that he fulfill it, or that he offer expiation?