Here's why:
* The League's Purpose is a Red Herring: The story initially presents the League as a genuine organization offering a lucrative job to red-headed men. This leads the reader and Sherlock Holmes to believe it's a legitimate opportunity, creating a false sense of security.
* The Real Motive: In reality, the League was a complete fabrication created by the villain, John Clay, as a distraction and a way to keep his target (the bank manager, Mr. Openshaw) occupied in the basement. This way, Clay could dig a tunnel from a neighboring building to the bank's vault.
* Misdirection: The focus on the League's seemingly benign purpose serves as a clever misdirection tactic. It throws both Holmes and the reader off the scent of the real crime.
By focusing on the League's seemingly harmless activities, the story creates a compelling mystery that keeps the reader guessing until the truth is revealed.