I absolutely do not agree with the idea that this is stealing. How can it be stealing, when the owner still has the thing that was supposedly stolen?

Different circumstances, different terminology. The correct terminology (see US Title 17 or CDPA 1988) is "infringing". Anyone who insists on using the word "stolen" is signalling their ignorance of the first, most basic fact of copyright law.

There are all kinds of violations that are not stealing.

If I point a gun to your face and take your money, that's a law being broken, but taking that money is not stealing, it's robbery.

If I threaten to expose some dirty secrets and demand money or things from you, that's blackmail but not stealing.

If I take your textual content and re-publish it under my own name, then that's an infringing use but again, not stealing.

The law you're looking for is ~copyright~. The fact that the work isn't actually stolen is the keystone in how you can take the copyright case to trial. It's pretty hard to prove infringement if you have no record of the original work (ie it's been stolen).

Stealing means the victim doesn't have the stolen item anymore.