Does the story of Demeter and Persphone promotes dualism, the notion that good and evil have equal powers?
Whether you consider the story of Demeter and Persephone to promote "dualism" in terms of notions of good and evil depends on several things. First, there is no singular entity, "the story of Demeter and Persephone." Instead, we have several important ancient texts, including the Greek "Homeric Hymn to Demeter" and the Latin Claudianus' "Rape of Persephone" that tell versions of oral traditions about these goddesses. In these, Hades seizes Persephone to be his wife. From an ancient point of view, this was not "evil"; the great hero Theseus seized Hippolyta the Amazon, for example. Hades himself is brother to Zeus and king of the Underworld as Poseidon rules the waves and Zeus the heavens. He isn't really evil per se -- he actually does far less in the way of seizing women (and young boys) than Zeus. These works should not be read anachronistically through the Christian lens. Hades is not Satan and Zeus not God, and Hades does not represent "evil" nor does Zeus represent "good". They are just anthropomorphic deities of the Greek pantheon engaged in conflicts of interest. Therefore it is not appropriate to say that these tales support dualism and give good and evil dualistic value.