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.
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!