Do humans own animals?
"Own" is a loaded word.
For domesticated animals we are legally responsible for what they do. If your dog bits someone, you will hear about it.
Partially domesticated animals like a feline? You aren't legally responsible for their actions because they aren't completely tamed.
Now, the owner of any pet knows that being owned means you are responsible for their care, their upkeep, their needs and in fact they pretty much ‘own' you.