One common theme between the Greek myth of Persephone and Demeter and that of Theseus and the Minotaur is the sacrifices that people or gods make for love and for causes greater than their personal interests.
In the first myth mentioned, Demeter is the goddess of the earth, and Persephone is her daughter. The theme of love and sacrifice is played out through Persephone’s abduction by Hades and the trade that Demeter has to make in order to restore the earth to fertility. The pomegranate seeds that the daughter eats correspond to months of separation. On one level, the myth can be interpreted as a representation of natural phenomena, specifically the functions of the seasons. On another level, however, by focusing on the difficult deal the mother has to make, we can interpret it as an expression of an adult exchanging their personal and family welfare for the greater, social good.
The other myth is concerned primarily with a male hero, Theseus, who is part god and part mortal, and a monstrous figure, the Minotaur, who is a combination of man and bull. Theseus’s role can be compared to Demeter’s in that he must try to save his country from hardship. In this case, Athens is annually sacrificing seven men and women to King Minos for the Minotaur to consume. Differences from the other myth are that Theseus kills the Minotaur and also abandons Ariadne, the woman who helped him get through the labyrinth. His leaving her behind could be compared to Demeter’s leaving Persephone; in both cases, their broader mission was to help society rather than focus on their personal needs.