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If you own a web site and believe that it is "stealing" for AI bots to read your site's content and learn from it, do you also believe that search engine indexing is "stealing"? Search engine indexing involves the search engine bot downloading all the public content of your site and building a model (the index) from it. That is how it's possible for search engine users to find your site.
If you do believe search engine indexing is "stealing", have you blocked Googlebot, Bingbot, BaiduSpider, DuckDuckBot, YandexBot, etc. in your robots.txt?
"Publishing" means making public.
If you write a book, you own the copyright to the book. But the fact that the text of your book contains a particular word, e.g. the word "mesothelioma", is a public fact. You don't own that fact.
A search engine for book content can read your book, and record the fact that it contains the word "mesothelioma" in its model; and then when someone searches for that word, it can return a link to your book.
Creating the index meant that the search engine internally made a copy of the text of your book. However, serving search results is not a copyright infringement; rather, it is stating the true fact that your book contains that word.
Similarly, if you write a book about how asbestos causes mesothelioma, that fact is not your property. If someone borrows your book from the library, reads it, and learns that fact, they do not owe you money. Even if they go around telling everyone about mesothelioma, they still do not owe you any money.
If they are an academic, the rules of academic publishing say that they are supposed to cite your work as a source — telling their readers that they learned something from your work. But if they don't, that's still not copyright infringement; it's plagiarism, which is not a crime but rather an offense against academic honor.
