I prefer to call people with pets guardians or stewards rather than pet owners. The reason for this is ownership suggests that the pet (animal) is a possession and not a sentient being. The other thing it suggests is that if someone owns an animal they don’t need to respect or honor that animal’s boundaries. This is far from the truth and not honoring an animal’s boundaries, can in some cases, provoke an attack from that animal in one form or another.
When I have used the words pet ownership it has been for SEO reasons, but I prefer the words pet guardian. Can we really own another sentient being?