This will slightly overlap with the other replies, but to be concise:
> If you put stuff out in public for anyone to use, then find out it's used in a way you don't like, it's your right to stop sharing
Yes. The entire point of Copyright and the reason it was invented is to ensure people will keep sharing things. Because otherwise people will just stop publishing things, which is a detriment to all. (Including AI companies, who now don't get new training data)
We have collectively decided that we will give authors some power to say "I don't like how my work is being used" to ensure they don't just "stop sharing".
Fair Use is an exception to that, where the public good does outweigh an individual author's objections. But critically, not such that authors stop publishing. Hence the 4th "factor" in US copyright law (which is one of the most expansive on fair use), where the "effect of the use upon the potential market for or value of the copyrighted work" is evaluated. Fair use isn't supposed to obliterate the value of the original work, or people will stop publishing again.
This is what makes AI training's status so contentious. In terms of direct copyright it is a very weak case. It is incredibly hard to prove a direct 1:1 copy from AI training data into the model and into the output, you have to argue about the architecture of LLMs, and it's incapability of separating copyrightable expressions from uncopyrightable facts.
Yet in spirit, AI training clearly violates copyright. The explicit stated purpose is to copy the works for training data, oft without any compensation or even permission, in order to create a machine that will annihilate the market for all works used.
People already are pulling back on the amount of works they share.