>Firstly publishing something on Facebook explicitly gives them the right to "copy" it. It certainly gives them the right to exploit it (it's literally their business model.)
This isn't necessarily true for a user content host. I haven't read Facebook's TOS, but some agreements restrict what the host can do with the users' content. Usually things like save content on servers, distribute it over the web in HTML pages to other users, and make copies for backups. This might encourage users to post poetry, comics, or stories without worrying about Facebook or Twitter selling their work in anthologies and keeping all the money.
>In school we read setwork books. We wrote essays, summaries, objections, theme analysis and so on. Some of my class went on to be writers, influenced by those works and that study.
Scholarly reports are explicitly covered under a Fair Use exception.
https://www.copyright.gov/help/faq/faq-fairuse.html
But also be careful not to anthropomorphize LLMs. Just because something produces content similar to what a human would make doesn't mean it should be treated as human in the law. Or any other way.