So you cannot train your drawing skills by copying other people's artworks?

You can do it in private, but you can’t distribute the resulting image, let alone sell it.

Then I don't really understand your original reply. Simply copying a publicly available image doesn't infringe anything (unless it was supposed to be private/secret). Doing stuff with that image in private still doesn't constitute infringement. Distribution does, but that wasn't the topic at hand

The most basic right protected by copyright is the right to make copies.

Merely making a copy can definitely be infringement. "Copies" made in the computing context even simply between disk and RAM have been held to be infringement in some cases.

Fair use is the big question mark here, as it acts to allow various kinds of harmless/acceptable/desirable copying. For AI, it's particularly relevant that there's a factor of the "transformative" nature of a use that weighs in favor of fair use.

You can train a neural network in private too and nobody will have a problem with that. The topic of discussion is commercial AI.

The answer is "it depends". Distribution is not a hard requirement for copyright violation. It can significantly impact monetary judgements.

That said, there is also an inherent right to copy material that is published online in certain circumstances. Indeed, the physical act of displaying an image in a browser involves making copies of that image in cache, memory, etc.