'T'would really help to know what the argument from your opponent is.
That said, why have public libraries? Shouldn't people buy books? Why have freedom of speech? (Preventing Glen Beck from opening his mouth, does have a certain appeal, but it would shut down Jon Stewart and Stephen Colbert as well.) Why allow science when we have religion? Galileo and Darwin are dangerous!
I would expect someone in the library business to be more in tune with the concept of both gratis and libre.
And, if it's fear of the unknown, then why have computers, recordings, or anything else in a library that was not hand-transcribed by a monk with a quill? The printing press is a tool of the devil!
Does the library contain any books on FOSS?