I agree that the "explanation" of the origin of ideas is also important. I love it when my students make a connection from mythology and see it's theme running in a current movie or television show. In addition to understanding the past, realizing that many key themes in life are "recycled" helps them recognize the connections between history and the present.
Mythology is important because it "explains" where many different ideas or origin have come from. Think about the story of Narcissus and Echo. My students love to hear fascinating tales about how things came to be. Origin study is always interesting.
As an aspect of ancient culture, the study of mythology is a study of classics, and history to some degree. Looking at the way stories were formalized and at the content of ancient mythology can tell us quite about about the people who created, wrote/recited and remembered these stories.
Additionally, we can compare the myths of the past with the myths of the present to assess how much or how little our lives have changed in the "grand scheme of things".
My curriculum that I teach has a mythology unit. At the beginning of the unit when building background with the students, I discovered that all of their working knowledge of classical mythology comes from Rick Riordan's Percy Jackson series. I am not kidding. It's actually really great, because the series has made them buy into the value of mythology and its importance. They actually want to know more about it now to deepen their understanding of Percy's adventures, whereas before the popularity of the series, most kids could have cared less.
If people should study mythology, it is only because it gives them a basic sort of cultural literacy. It allows people to understand what other people are talking about when they say something like calling something a "Herculean task" or calling something a "hydra-headed monster." Outside of that, there is no practical reason to study mythology.
Students should study mythology for some of the same reasons they should read novels. Mythology is entertaining, like novels. Mythology tells us a great deal about the views and life of those who wrote it, like novels ( an author is alive in their work). Mythology tells us about what we think of today as "pop culture". If we look at the works on the NY Times bestseller list, we can glean some great information about the reading public. If we look at books with the highest sales, we know what people are interested in and likely relate to. Mythology is the story of the masses in the same way novels are the story of today's masses.
Students should study mythology because there are numerouse allusions to mythology in the classical works as well as modern works. Mythology gives one an insight into the culture, into the beliefs before Christianity took over; and it gives insights into the psychology and sociology of the past. Mythology also gives us a look at how democrary came about in Ancient Greece. It show us how people explained nature before science was able to explain nature. Mythology is expecially interesting and studied by students of literature, phychologists, and theologians. The purpose of studying mythology can be summed up as education, explanation, and entertainment.