It should reassure such people that the library also throws away books that it has bought. At my library that's my job, discarding the books we no longer want, use, or need.

This is called Weeding:

Textbooks, exam books, multiple copies of outdated computer books, all go into the trash. If its more than ten years old, it gets pulled. If it doesn't get enough checkouts and we have multiple copies, it gets pulled. Why? To make room for new stuff. Libraries have limited shelf space and a hefty budget for new books, that if we don't spend we won't get the same amount next year.

If it can be sold it will be sent to the library bookshop, and even they are particular about what they put on their shelves.