it doesn't really matter, does it? its whatever they consider quality. You would use your own definition if you wanted to do the same. I collect certain kinds of art books, and fantasy novels. If you liked something else, like computer science academic books, you could collect those. It's up to your own definition and style.
Does it matter? No, it really doesn't. I'm just curious, as someone who has a few hundred books sitting around the house, plus another 20-50 checked out from the library at any one time.
I don't know that I'd consider much of any books I own to be "quality". But the house I have does have a fairly nice built-in bookshelf that could probably hold 500 books all by itself. Someday I'll fill it, maybe? With mass-market paperbacks and hardbacks? "Quality" books? Who knows!
It's a personal judgement. What you find quality and what I find quality is likely very different, so asking them to justify that their books are quality seems to be some sort of pedantic attack.
