Now, in theory, you learning from an author's works and competing with them in the same market could meaningfully deprive them of income, but it's a very difficult argument to prove.
On the other hand, with AI companies it's an easier argument to make. If Anthropic trained on all of your books (which is somewhat likely if you're a fairly popular author) and you saw a substantial loss of income after the release of one of their better models (presumably because people are just using the LLM to write their own stories rather than buy your stuff), then it's a little bit easier to connect the dots. A company used your works to build a machine that competes with you, which arguably violates the fair use principle.
Gets to the very principle of copyright, which is that you shouldn't have to compete against "yourself" because someone copied you.