Three articles later, he quotes Aristotle to the effect that "to love is to wish good to someone," from which he draws out two kinds of love: the "love of friendship," for the person you wish good; and the "love of concupiscence," for the good you wish someone.
Friendship, meanwhile, can be of three kinds: "that which is founded on 'usefulness,' that which is founded on 'pleasure,' and that which is founded on 'goodness.'" But "friendship of the useful or pleasant, in so far as it is connected with love of concupiscence, loses the character to true friendship."
To find out what St. Thomas means by "true friendship," we move to the article "Whether charity is friendship" in his treatment on charity as a virtue (as distinct from love as a passion). There, he writes:
... not every love has the character of friendship, but that love which is together with benevolence, when, to wit, we love someone so as to wish good to him....
Yet neither does well-wishing suffice for friendship, for a certain mutual love is requisite, since friendship is between friend and friend: and this well-wishing is founded on some kind of communication.
Which, clearly, brings us to the matter of loving our pets.
The thing about this love of true friendship is that, because it's founded on some kind of communication, it involves something being communicated to a person, so that a person becomes like the friend he loves. Does that mean you can't love a scoundrel without becoming a scoundrel? If you love him for being a scoundrel, yes!
And if you love your dog? Then you become like your dog.
That may not be such a bad thing, depending on the kind of person you are. If you love your dog for his loyalty or good cheer, that could make you more loyal and cheerful. You may love your dog for his sheer doggishness, which is probably more of a friendship of delight than the friendship of goodness St. Thomas has in mind when writing of charity.
But you can also love your dog in a way that communicates canine nature to you, if you will. This is a bad love, because canine nature is beneath human nature. What often happens, I think, is that an owner tries to communicate human nature to his dog, and thinks the dog is communicating human nature back to him. Humans, though, cannot communicate their nature like that; it's one of the signs we aren't God.
I suspect there's a general reluctance on the part of Christians today (in the West, at least) to accept the consequences of our place in creation. We seem to be slumming among the things that are beneath us -- not just because of the concupiscence that always has led humans to improperly love created things, but because of a false modesty (which may not be recognized as false) about what we are.
In a comment below, Neil Dhingra quotes Metropolitan John Zizoulas, who refers to mankind as "the priests of creation." That's true, but it's a priesthood in which the priests really are closer to God. We really are made in the image and likeness of God. We can never wholly efface that image in us, nor can we transfer it to other things in creation. We do neither us nor the rest of creation any favors by forgetting this.