The typical response from Joe Public after hearing a rumor about deaccessioning (ie: throwing away books) is general horror. Something along the lines of "how could you possibly throw away a book, someone might want to read it?!" and "how could you possibly ask for more money WHEN YOU ARE THROWING AWAY BOOKS?!"
Folks, it's an issue of shelf space. If the books are digital, keep them for whatever, why not. If they are physical, old books need to be tossed when new books are in.
Yes, it makes us librarians wince a bit every time, but it's a simple matter of necessity. We need space for new books, so we throw out the old books that aren't being used.
Sure, you can make exceptions (that's more of a management issue). But, right, space. Unless you can figure a way to put in more shelving, you're going to have to throw some things away.