Actually, she's a lot more correct than you can apparently conceive:

You said:
"do domesticated house cats buy their own food? No. Their OWNER DOES. What happens if you stop feeding them? They die."

And generally, that's wrong. If a cat is unhappy with the owner due to lack of feeding or treatment or not getting along with other cats, they leave. I've known several cats who left their owners and went to live somewhere else and sometimes they came back later. So of course you have to feed your cat. That's what a servant does and if you don't serve your cat well enough, it will cease to grace you with its company.

And you said:
"did your cat purchase YOU at a pet store, or adopt you from an animal shelter? Because that's the only way it could be considered YOUR owner, in any sense (legal and logical)."

But plenty of cats do choose their owners. They show up on someone's doorstep and the person ends up adopting them. That is the story of literally half the cats I know.

And you said:
"You know when your cat sits up on a high place and looks across a flat piece of ground?" Yes, I do. And if it happens to be in the way, like in front of my screen when I'm trying to type, then I lift the damn cat off the table and put it on the floor. Because I own the table AND the cat, no matter what it might "think" (I find it interesting that you seem to have some magical insight into the feline cognitive process)."

That's not what she's talking about. She's talking about the high perch in the house, not in front of your screen. The screen situation is when the cat wants your attention.

And finally:
"I guess I'll stop there, you did a good enough job of looking like an idiot on your own and I've reinforced that fact."

If you read the comments that followed your post compared to what followed her post, it's clear who looks like the idiot here.