Why should people today care about greek mythology ?

Becuase all of us are descendants from that time and we don't know what was real and wasn't real at that time

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.