It is a shame that the word anti-library is used so incorrectly. A library is a collection of books, periodicals, etc., especially when organized; therefore, an anti-library would be an empty space where books, periodicals, etc. are not kept. I cannot imagine boasting of having an anti-library.
My library is in constant churn. I buy, read and (usually) donate to the local library. I only retain those books in my specific interest areas and they change as the interest areas change. I refuse to let money sit unused in books I have no expectation of reading.