Because while in the Underworld during her first stay with Hades she ate some pomegranate seeds. Eating them bound her to the Underworld, and she must return to it for half of the year, and is able to be with her mother and the living for the other half of the year.
She had to return to the Underworld because she had eaten food from the Underworld (a pomegranate), which bound her there.
Because she tasted of the food of Hades, a handful of pomegranate seeds, she was forced to forever spend a part of the year with her husband in the underworld.
Persephone ate of the pomegranate in the Underworld, and thus every year must go to the Underworld - then return to Earth.
In Greek myth, it is because of the abduction of Persephone that the Earth/we know the seasons: for Persephone also ate of the pomegranate in the Underworld and every year must return between Earth/Olympus and Underworld.
Persephone, as a figure in Greek mythology, has not made direct contributions to the modern world. However, she continues to be a source of inspiration for artistic and literary works, as well as symbolic interpretations related to seasons, growth, and transformation. Her story is often used as a metaphor for the cycle of life, death, and rebirth.
Demeter greets the return of her daughter by bringing spring an summer. When Persephone must return to the underworld, fall and winter begin.
It isn't really Demeter who saves Persephone, but Zeus. After Persephone is abducted by Hades, Demeter (the goddess of the harvest, and mother of Persephone), begins to neglect her duties. Humans begin to go hungry, so Zeus sends Hermes to the underworld, to talk to Hades. (Hades gives Persephone back, but she has eaten in the underworld and must return for a period each year. This myth explains the winter.)
It isn't really Demeter who saves Persephone, but Zeus. After Persephone is abducted by Hades, Demeter (the goddess of the harvest, and mother of Persephone), begins to neglect her duties. Humans begin to go hungry, so Zeus sends Hermes to the underworld, to talk to Hades. (Hades gives Persephone back, but she has eaten in the underworld and must return for a period each year. This myth explains the winter.)
Persephone's year is divided between Earth/Olympus and the Underworld.
Persephone was the daughter of Demeter, a goddess of growing things, and Zeus had promised Hades for Persephone as a wife - he then took the maiden when she was grown, unknowing that neither Persephone or Demeter had not agreed to the marriage promised to him; Persephone became his wife and Queen of the Underworld either by choice or Hades tricking her when she ate of the food of the Underworld. Doing so ensured that she must every year return to the Underworld.
She had eaten 6 pomegranate seeds after being kidnapped by Hades and if you eat food in the Land of the Dead, you must remain there. Therefore Persephone must remain in the underworld for 6 months of the year.
Because she ate the seed's of a pomegranate (the food of the dead) and Hades said she must stay in the underworld.
The most popular is in which Hades asks Zeus for Persephone's hand in marriage and is granted it, while Demeter does not know and when Persephone is taken he offers her the pomegranate to eat in the Underworld. Which she does, thus she can't leave the Underworld save for part of the year. Demeter has been searching for her daughter, and finds out where Persephone is, and demands her return; when Zeus and Hades argue that Persephone must stay in the Underworld for a portion of time; Demeter lets the world feel her wraith in the first winter.
The ancieant myth about Persephone and Hades states that any living thing that eats food from the underworld must remain there for all time. Perssphone did eat six pomigranet seeds however, and therefore must spend six months of every year in the underworld. This myth was used by the Greeks and Romans to explain winter (Persephone was the goddess of spring and growing things)