The argument for 'fair use' in DVD copying/sharing is much weaker since the thing being shared in that case is a verbatim, digital copy of the work. 'Format shifting' is a tenuous argument, and it's pretty easily limited to making (and not distributing) personal copies of media.
For AI training, a central argument is that training is transformative. An LLM isn't intended to produce verbatim copies of trained-upon works, and the problem of hallucination means an LLM would be unreliable at doing so even if instructed to. That transformation could support the idea of fair use, even though copies of the data are made (internally) during the training process and the model's weights are in some sense a work 'derived' from the training data.
If you analogize to human leaning, then there's clearly no copyright infringement in a human learning from someone's work and creating their own output, even if it "copies" an artist's style or draws inspiration from someone's plot-line. However, it feels unseemly for a computer program to do this kind of thing at scale, and the commercial impact can be significantly greater.
