Earlier quoted context omitted.
When you train a GenAI on an image, legally speaking you're training it on a COPY of that image. If you intend to train a GenAI on a copy of an image I own the rights to (perhaps because I created it), then you have to negotiate with me. If you don't, then you are violating my copyright.
That's not how copyright works. Copyright law limits creating copies of a work, not interacting with copies of a work lol. Which means it doesn't apply to training. What you're describing is some totally new law that doesn't exist anywhere on earth, because it would make no sense. Imagine if an aspiring artist who's training by studying a copy of another artist's drawing, or by listening to a copy of another artist's…
When you are downloading someone's copyrighted music to train your GenAI with, the act of downloading it creates a copy of the work that now exists on your computer.
The essence of copyright law is to give the owner the right to decide how copies of their work are used, which you have violated if you did the above without their consent. Incidentally, this is why pirating music is a copyright violation.
Your argument is based on falsely equating the process of a human getting inspired by prior art to training GenAI on the same. If a human goes to an art gallery and gets inspired by some copyrighted work, he did not have to create a copy of that work for the inspiration to take place.
On the other hand, with GenAI training, the act of creating a copy is unavoidable (e.g by taking a picture of a painting, which is uploaded to your computer, which is piped into a training algorithm).
The human's mental representation of the painting does not count as a copy, but painting_photo.png does and the owner's rights fully extend to it.