Son of the Woods

Hippolytus, young prince of Athens and son of Theseus, has been confessed to by his step-mother. Horrified by those incestuous feelings, he runs away, to find peace in the woods he is used to hunt in. But as he tries to cope with the situation he just went through, a question arises in his mind: when Phaedra, his step-mother, after revealing her passion, begged him to stab her... why did Hippolytus not kill her?