First I’d think very carefully about whether your relationship either your dc is more or less important to you than your gc beliefs.
The teenage years are very difficult. They’re pulling away. They’re looking at us as a model for what they don’t want to be, because the drive to differentiate is biological, innate and overpowering. It hurts as a parent but everything is unfolding just as it should.
If your gc beliefs are fundamental to you, tread lightly. Don’t show your hand too directly, because if you do, it could be the defining point of differentiation.
If your relationship with your dc is important, listen to them with interest and curiosity about who they are right now, how they arrived at a point where throwing out books felt necessary. Don’t challenge or correct, just listen. They’re on a journey but you don’t know the destination. They’re path is completely different to yours so let them tell
you about the scenery.
Listen to their feelings and empathise because that’s the crux of relationship.
Don’t poke holes in their logic - they’ll notice the holes as they try to explain, so don’t distract them from their internal critic or else they’ll only hear the critic speaking with your voice, instead of their own.
It is absolutely crucial that they hear their own doubts, and not just on this issue. This is a vital life skill.
It’s very likely that their position is driven my empathy, a sense of injustice - those are great things so don’t belittle them.
When the logic fails (as it will) steer them back to their feelings and support them. If they only learn that you can disagree and still love each other, they’ll have learned something profound.