The study of Greek mythology provides a greater understanding of Greek history and college, increases literacy through use of words with Greek roots and helps readers understand the many allusions made in other literary works. An understanding of Greek mythology is an essential part of an education in the classics or humanities, but many would argue that having at least a fundamental understanding of the basic Greek myths serves a person well in any specialty.
One of the main arguments against Greek mythology as a curriculum requirement is that it is entirely fictional and not part of historical fact. While the myths themselves are not true, they were a major part of ancient Greek history and were often a reflection of the fears and triumphs in life. Understanding Greek mythology, the religion of the time, helps understand the culture as much as learning Christianity or Hinduism helps form an understanding of those cultures.
Greek mythology introduces readers to Greek words or root words that can help deduce meanings of English vocabulary that utilize those root words. When readers encounter words with the root "homo," for example, familiarity with Greek myths can help them understand the word has something to do with sameness.
Greek mythology is alluded to in many other great classic literary works, from William Shakespeare to James Joyce. Modern literature also borrows from Greek mythology, as in the young adult stories about Percy Jackson. Even outside the classroom or literature, movies, television shows and even common idioms frequently allude to common Greek myths. All of these allusions would be lost on a person who did not have an education in Greek mythology, which would greatly hinder his experience of the world.
Outside of educational benefits, many readers simply enjoy the fantasy of Greek mythology.