I don't know if every practitioner believes the same thing, but from what I've been taught, you can't choose your familiar like that. A familiar is an animal almost destined in a way to help with your craft. Your cat is your pet, a familiar animal would come to you. I believe there are summoning spells for familiars, but I don't think you can legitimately perform a spell that makes a pet your familiar. Also, you don't need a familiar, it's not required unless you want one.
If anyone learned differently or believes something different, let me know! I personally don't have a familiar and that's what I was taught about them, so that's what I go by.
A familiar is not [just] a pet, indeed. In fact, the term 'familiar' is short for familiar spirit. There are plenty who will insist a familiar is not physical whatsoever. And there are those who will cite cases of witches in Europe who did actually have pets who they insisted helped in their workings.
But the point is more this: A pet is a pet. Cats will get in the middle of your tarot spreads and spells, because it wants attention and you're paying something else attention in stead of a pet. Dogs may do similar. It's a very consistent thing with behaviors of these animals, and a lot of practitioners lean on confirmation bias that suddenly, even though the animal does the same thing with other activities, and even though other pets did the same thing before they began to practice witchcraft or magic, that it's suddenly a special thing. It is not necessarily so.
A familiar spirit, whether purely metaphysical or whether housed within a physical pet, works as an actual adjunct to a person's magic practice. Familiar provide protections, act as wards and tells (as in alerting to a visitor who should not be wanted for example), and runs errands. A cat sitting in the middle of a tarot spread to lick its paw or just stare at you is not a familiar.
