1. For the same reasons those old guys studied them.
2. You'll get a lot of references.
3. You'll learn about the cultures and ideas of the myth-makers.
Here's a great example from Cherokee mythology (warning: you can't always trust the Internet when it comes to Native American traditions, because some people think it's cool to just make stuff up and publish it). The First Woman in Cherokee tradition was Selu, Corn Woman, who is "resurrected with each harvest." This tells you a lot about the importance of agriculture--particularly the growing of corn--in Cherokee culture. It also paints a picture of the connection between growing food and life, since Selu's life is connected to the corn harvest.