The actual core of the problem is described here and predates the discussion on the Emergency Library:
https://nwu.org/book-division/cdl/faq/Summary from Wikipedia: https://en.wikipedia.org/wiki/Controlled_digital_lending
> Opponents of CDL argue that CDL is not like lending, which does not require copying, and dispute the claim that only one copy at a time is available for reading. Opponents say that CDL involves first making an unauthorized digital copy of a printed edition of a work, and then making an additional unauthorized digital copy for each "borrower". Opponents also argue that unencrypted digital copies are distributed for viewing in a Web browser, and that these copies can be retained, viewed, or printed from the browser cache even after the e-book is marked as "returned" and is available for "lending" to other readers.
This is based on the vague notion of "creative work" in copyright.
Before the digital age, there was only a close 1:1 relationship between the ephemeral/conceptual creative work and physical copies of that work. Authors - and more specifically publishers - held exclusive control over the latter since the act of copying and distribution was prohibitively expensive.
The game changer in digital technology is that it democratized creating and distributing copies. Not just that, digital technology has blurred the definition of a "physical carrier" as a creative work can be represented as set of constituent bitstreams on a disk but also as pixels or audio on a screen/speakers. The creative work itself is re-generated/re-constructed through digital devices each time it is consumed.
Copyright still applies, the ephemeral conceptual work as was original intended by the author is still protected. But it's become very difficult to apply that protection to equally ephemeral representations in the digital realm.
The hard problem then is that copyright doesn't make a distinction between "physical copy", "digital copy" and the ephemeral "creative work" as an abstract idea or concept which was originally conceived by the author.
This leaves an huge void for interpretations. And so, both the Internet Archive as well as the Authors Guild can make sound legal arguments.
You'll find the "copyright is broken" cry on both sides of the aisle. But I don't think that rings entirely true either. There are enough provisions for publishers and authors to authorize or take down published copies online. The Internet Archive in particular even openly allows for that through their digital front office. The bigger question remains how the digital era shapes publishing and lending business models.