Why does the Essential X-Men Volume 1 TPB not start with The X-Men #1?!
Question: (the series that was later renamed Uncanny X-Men)
Answers: (the series that was later renamed Uncanny X-Men)
Thats because some of their earlier adventures were already reprinted under Classic X-Men. X-Men #1 itself was reprinted quite sometime back.
It starts with the Giant Sized comic because that's the first appearance of the All-New, All-Different team of Wolverine, Storm, Colossus, etc.