(1) When I use phrases like "my cats" in my writing, I do not mean to suggest that they are objects I "own".
Yes, I am responsible for them in many respects, but as they are living, sentient creatures, they are not really "ownable", at least as far as I'm concerned.
Hence, wording like "my cat" or "I have four cats" should be read here as similar to when people say "my sister" or "I have four cousins".
Also, I don't like the word "owner". I prefer to consider myself "my cats' human" in the same sense that said felines are "my cats".
(2) My personal definition of the word "person" most definitely includes members of the feline species. "Person", in my mind, is not necessarily synonymous with "human", but rather a term that when used connotes (for me at least) a certain measure of respect, and which acknowledges the sentience of the individual in question.
Of course I don't believe that cats perceive the world and interpret information exactly the same way humans do. But I also don't believe that humans have the monopoly on how to do self-awareness. Cats are different from us but that doesn't make them nonpersons.
Hopefully that makes sense. I know some people don't care about making such distinctions, but I do, so I figured I should explain.