I don't see a different between the word "pet" and feelings and attributes you guys are saying.
I've had pets my whole life, and I have a pet cat. Having a pet (versus having an animal, say, or 'raising animals') implies all the responsibility, love, heartache, and care that we put into them and receive in return. I don't ever doubt that my friends with pets feel the same way. Maybe it's the descriptivist in me.
Though, personally, I do prefer the term 'companion animal', but don't have any problems with the ownership. This is my
cat, and I'm not giving her up to anyone. I love her, but she's not smart enough to make good choices on her own (eating nothing but cheese, never seeing the vet, defenestrating herself, practising kitty parkour in the glassware, etc). I own her because I control her life in a way I could never control another human or creature I didn't own.
I guess its sort of like how I prefer to call my husband (well, technically long-term comman-law-husband) my 'partner'. "Husband" and "Wife" have too many negative, religious, and gender/sexually oppressive connotations for me to use comfortably.