> Animals want to be free like any other living being,
That's a nice thought, but in reality there are plenty of humans even that just get overwhelmed and scared at the thought of freedom, whether their own or other people's, and actively demand, seek, and create rigid and oppressive systems of rules and restrictions in order to trade freedom away for predictability. Otherwise… The entire human world would likely be shaped quite different from how it currently is.
Our morals don't map cleanly onto physical reality, and values like "freedom" are unfortunately still relatively inconsequential next to causalities like "death", "killing", "starvation", and "culling". Does a tapeworm "want to be free" from its host? How about a male anglerfish, which only has a nervous system complex enough to find a larger female anglerfish which it can latch onto while its entire body is subsumed away? Animals want whatever animals are neurologically wired to want, humans included, and only sometimes does that align with our higher ideals of life having intrinsic worth. The nature of things simply is, and in a lot of cases, I think the ways we try to assign moral judgements to it are projecting our own social instincts onto ecological and cognitive systems that do not share our values.
Certainly, the power dynamics, amount of control, and relative levels of awareness between humans and pets are… Would be rightfully horrifying, though, if the alternative were a relationship of equal peers.