He does not care what she remembers. He tells her his story. He tells her that her mother was virtuous and she should be too. He wants her to know the importance of chastity and the continuity of his line. Her only reason to be alive is to rear children and guarantee the continuance of his blood.
Women are objects to be possessed.
Prospero uses Miranda as a puppet to gain power. At the time the novel was written, women were only objects and not humans, and that is obvious in The Tempest .