1957 "Carnival of Books" Interview is a recorded interview with J.R.R. Tolkien on January 15, 1957, for the NBC radio show "Carnival of Books", hosted by Ruth Harshaw. An extract was published in The Annotated Hobbit: Revised and Expanded Edition on page 210; in it, Tolkien mentions why he used spiders in The Hobbit.
Extract
"I put in the spiders largely because this was, you remember, primarily written for my children (at least I had them in mind), and one of my sons in particular dislikes spiders with a great intensity. I did it to thoroughly frighten him and it did!"