"No, the point is that a library catalogue enables access to the content. As does a hyperlink. To replicate the situation physically, let's do a thought experiment: it would be possible these days to build a library with a robot to fetch a book off its shelf and put it on a desk for you to read (there are modern warehouses that fetch stock and load trucks this way). Would that breach copyright?"
No, because we do not have a matter replicator yet. Following the hyperlink produces a COPY of the target in question. Since COPYing is involved, copyright is automatically invoked.
"Libraries do have exemptions, but only for educational or non-commercial use. You breach copyright when you photocopy the book to avoid buying it."
That's YOU, though, not the library. They're exempt from the redistribution restriction, for example, because (a) they're usually public, as in government-run, facilities, and (b) that's their purpose for existing: a middle ground between full lock-and-key and full public domain, a way to allow some additional exchange of information as mandated in the Constitution while still respecting copyright that helps to encourage new works being made. Rental houses an Redboxes have to buy special rental copies of movies at higher rates from publishers (so that publishers recoup lost sales), but libraries don't always have to, especially if some of their stocks are donated.