Why does the White Witch want to capture and kill any "Sons of Adam" or "Daughters of Eve"?

One reason that is given for her wanting to capture and kill any "sons of Adam" or "daughters of Eve" is because of the prophesy. It is said that 4 humans will sit on the throne which inevitably leads to the destruction of the White Witch. In order for her to keep her power and the curse she has on Narnia, she has to make sure the prophesy doesn't come true. This is why she is determined to kill the children.