If I may ask, do you mean things like zoos, or are you also against people caring for cats, dogs, etc? Or are you fine with people having pets provided they're not caged?
For instance, I currently have 3 cats. However they come and go as they please as we have several pet doors. One of them doesn't really go out ever, another one I can spend several weeks without seeing. I don't consider them trapped or caged, but I do know that some people oppose the idea of pets to begin with, and I'm curious whether it is what you mean.
At least I am assuming you're talking about non-humans right now. Usually, using quotation marks around the word "pet" in a BDSM thread means human submissives, but it seems that's not what you mean, or am I misunderstanding you?