Why did the false mother, after being offered the child by the real mother, suddenly declares she wants the baby dead?

Answer:

Two prostitutes lived in the same house. One gave birth to a son and the second gave birth to a boy three days later. However, the second woman's child did not survive the night, so in the middle of the night, she swapped her dead son for the living boy. Of course, the first woman quickly figured out that the dead child in her bed was not hers. Thus, the case was presented in Solomon's court (I Kings 3:16-22).

Solomon points out that we have two people making opposing claims with no witnesses. They didn't have DNA tests back then. Solomon orders the living child to be cut in half and each woman was to be given half. (I Kings 3:23-25).

The real mother doesn't want her son dead, so she was willing to give up her son rather than see him die. The other woman is jealous of the fact that this woman has a child while hers is dead. She believes Solomon's "solution" will even her imagined score. While the two statements are presented one after another, you should understand that these two reactions happened at the same time when Solomon gave the shocking order. It was the shock of the order that brought what was hidden to light (I Kings 3:26). Neither woman had time to consider what she said or the consequences of her words.

The woman who valued the child's life was clearly the true mother (I Kings 3:27-28).