Disney owns the 1992 production of Aladdin so who exactly are they "stealing" from?

https://en.wikipedia.org/wiki/Aladdin

The argument, as I understand it is that the "theft" is in quotes because it's not literally copyright infringement, but fair use of an old public-domain folk tale that ends up consuming the latter.

Today, when kids know "Aladdin" they know the copyrighted/trademarked Disney character, not the traditional folk tale- that's the "theft" that happened.

Doesn't this mean that anyone can make a competing Aladdin story, though? Since they don't own the source IP?

It does! but you can't use anything Disney added (the tiger, the talking bird, etc..) and your production values would have to be super high to avoid looking like a store-brand knockoff. It's hard to deny that the Disney version does damage the original story in some way

If you subscribe to any concept of the public domain this is surely in it.

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Would most kids around the world even know Aladdin if it wasn't for the Disney copyrighted movie?

Aladdin, Ali Baba and Sinbad the Sailor were well-known long before Disney.

There's even a major Chinese company named after one!

Very likely yes. I was very familiar with this story, and other "Arabian" tales, well before Disney made the original animated version.

We also had Grimm's fairy tales, which I loved reading, and nowadays am reading to my daughter, to her delight. Yes, with beheadings and child-eating monsters and witches.

I assume he's saying Disney owns the 1992 film so the 1999 film is not theft, but he wants it to be because he doesn't like the 1999 film. Thus the quotes.

That's not a charitable reading of the comment, and furthermore, it's not even a reasonable assumption. Other comments clarify that the "theft" is in quotes because it's a figurative theft, not from Disney to themselves, but from Disney to the earlier, non-copyrighted folk tales it drew inspiration from. And the "theft" is that the Disney IP supplanted (via ubiquity) the public domain versions to the point lots of people aren't even aware they exist. Nobody is arguing it's literal theft, hence the quotes.