Learn English – what can we call someone who gives false promise to someone repeatedly but intentionally break the promise

There are several possible answers;

If this behavior is intentional - they may be a "saboteur" (one who sabotages), they may be "deceitful" (deceiving or misleading others), "suborning" (inducing (someone) to commit an unlawful act) or "malicious" (intending or intended to do harm).

If it is unintentional - then they are "mistaken" (wrong in one's opinion or judgment), "incorrect" (not in accordance with fact; wrong) or possibly "out-of-date" (no longer useful or acceptable) or even "out of touch" (not keeping informed of the developments relating to someone or something).

'Calumny' is close, though it's a legal term, and it refers to making statements wreck someone's reputation (which can't be done if it's done in private.) 'Slander' is probably better. 'Libel' is no good, as it happens in a publication.