So why pets in Romance novels??
Cats are very good judges of character. Dogs are too, but they often will sell their high standards for pats and a ball of raw hamburger. In other words, they are so hungry for attention, hungry for a big mac, that they will make pals with some serious jerks. I have known dogs to be very loyal, slavish to the point they would kill for their masters, die for them, yet the man was very unworthy of that adulation and devotion. Doggies are the accolites of some really ugly people--and I don't mean looks either.
Men tend to favour dogs because they are so easily controlled. This baseline programming of need for approval causes the dog to do tricks, fetch and will let an owner order them around. Men love to control things, so a pet that does as they are told, precisely as they are told, reinforces the male's need to be alpha leader of the pack.
Cats are too much like women. You need to earn our trust, our approval. Oh, we like attention, to be stroked, given goodies, but that doesn't mean we accept just anyone. Cats are caring, they give you room to make mistakes, but they want an equal. Cats are high maintaince and have high standards. They are picky about whom they give their affection to, and while it's a myth they won't come when you call them, they are not willing to perform like a dog.
Cats RULE. Man and woman are their servants. So males don't warm to this relationship. Men who respond to cats are worth looking at. If I were still dating and a cat didn't like my date, I would pay attention. On the other hand, when a cat takes up quickly with a man, the kitty is saying this is a person worth being friends with.
I used this "device" to clue in my readers about my heroes inner character, that he is worthy--even when the hero might not think so himself. Take Desmond Mershan from The Invasion of Falgannon Isle. Des is a wounded animal, a lot of pain inside him, pain for years, and it's driving him to be hard, sometimes uncaring, calculating. He comes to Falgannon to extract vengeance for his family. Instead of stopping the story and blethering how Des was hurting, yet inside was really a good man (i.e. telling the reader Des is this way), I opted to let The Cat Dudley demonstrate this. Dudley hates everyone. He is lord of Falgannon Isle and is used to getting his way. His immediate acceptance of Des, and Desmond's reaction to the cat, SHOWS the reader that Des is good inside, even when they may think Des is cold. Des storms into B.A.'s world, intent on destroying it, no regard for her or the people the isle. It would be rather easy to set the reader against Desmond. The fact that Dudley instantly loves Des and Des is charmed by him, it's out of character for the high-powered business man. A clear clue to the reader.
Thus, The Cat Dudley immediately tells the reader Des is a man above others. They warm to the hero and cat bonding, that keeps them liking Des, trusting he will grow and become a better person, the real person inside him.
Thus, having an animal in books is often more than just having a character with fur. They are an excellent way to show to the reader a person's true nature. If someone looks at a cat and the cat hisses and runs, that is worth more than a thousand words.