This is absolutely because they pulled the emergency library stunt, and they were loud as hell about it. They literally broke the law and shouted about it.
I think that you are right as to why the publishers picked them specifically to go after in the first place. I don’t think they should have done the “emergency library”.
That said, the publishers arguments show they have an anti-library agenda that goes beyond just the emergency library.
Libraries are allowed to scan/digitize books they own physically. They are only allowed to lend out as many as they physically own though. Archive knew this and allowed infinite “lend outs”. They even openly acknowledged that this was against the law in their announcement post when they did this.
The trouble is that the publishers are not just going after them for infinite lend-outs. The publishers are arguing that they shouldn’t be allowed to lend out any digital copies of a book they’ve scanned from a physical copy, even if they lock away the corresponding numbers of physical copies.
Worse, they got a court to agree with them on that, which is where the appeal comes in.
The publishers want it to be that physical copies can only be lent out as physical copies, and for digital copies the libraries have to purchase a subscription for a set number of library patrons and concurrent borrows, specifically for digital lending, and with a finite life. This is all about growing publisher revenue. The publishers are not stopping at saying the number of digital copies lent must be less than or equal to the number of physical copies, and are going after archive.org for their entire digital library programme.
No point asking them to justify why they have to ask, they probably don’t even know. Just say “Sorry, I don’t give that out”. I’ve never had a store push back after that - they probably get it all the time.