"We saved those books for you. That's what we do." Unfortunately, that perspective on librarianship is becoming as hard to find as books on vacuum tubes. The more common approach is, "We facilitate access to information. So that our library can be more modern and spacious, we got rid of OUR copy, but you can rely on databases or interlibrary loan to get that item." Meanwhile, every other library has made the same decision to "weed" that item. In my own research, I'm increasingly encountering items which were commonly available a just a year or two ago, but are now not available from any library (and yes, I've looked on WorldCat and its brethren).
What items get weeded from a library? When I've personally observed the weeding practices of my local libraries (public and academic), actual circulation is rarely considered, and utility or rarity or ILL availability is never considered. The official weeding policy of the library notwithstanding, weeding is all too often a 1-to-3-second judgment based on the age and condition of the item, a judgment made by one specialist librarian who is being graded on weeding productivity.
Sad weeding decisions I've witnessed recently: Classic childrens books weeded because "the book is older than the child." Brand-new (copyright 2011) books weeded because they are part of a collection that is being discontinued. Reference books weeded because other libraries do NOT have the same book (standardization, y'know). Short-run local history books weeded because the cover was dirty or because the book was old. Electronics books weeded because "no one needs that stuff." Paper journals weeded when I know that the digitized version is missing some of the content.