Why is a detective called a gumshoe?

I have never heard of a detective being called a gumshoe.

AnswerBecause they used to wear shoes with gum (soft and quiet) soles so they could sneak around and not be heard by the sound of their footsteps.

As often with slang, because of a joke: as both a detective (because he sneaks) and gumshoe (because they are useful to sneak) are called sneakers, so a detective is called a gumshoe.

"Alfred Hitchcock's latest mystery melodrama, "Vertigo," is all about how a dizzy fellow chases after a dizzy dame, the fellow being a detective (...). Slowly, the gum-shoe (sic) realizes that, somehow, this dizzy dame has spells (...)". (Bosley Crowther, "Vertigo", New York Times, May 29, 1958)