Well, why would they? At risk of horrifically simplifying things, I have a company, I decide I want some more money. I sell you the right to vote in some things that concern the company, and I sell you a share of any dividends that get paid out in the future. That's what you get. Do you now own the company? Do you own the company assets? I didn't sell that to you. I sold you the right to vote in some company meetings and decision making processes, and I sold you a piece of any future dividends that get paid out to you and others like you. Doesn't sound like "owning" something to me.
What does that mean? You don’t “own” the company, do you?
If the company is just me and a bag of tools, fixing people's cars on their driveway, do I own that company? What does it even mean for me to "own" it?
An opinion of mine the ownership of a company through stocks is secondary to stocks being a quasi-cash financial instrument like bonds.
But I don't get the "shareholders do not own business corporations" bit. Would a sole owner "own" a business corporation? Do real estate owners "own" real estate or do they own "bundles of intangible rights"?