Whenever we look at our civilization, our history and our creations as humans, we undoubtedly feel a sense of dominance. We pacified most of the land on our world; we are exploring the universe more every day, and our knowledge surpasses that of any other creature on Earth. However, although we may have the highest IQ, we don't rule the world, pets do.
You may be thinking, "Wait, no dog could invent marvels like agriculture, combustion engines and artificial intelligence. This is ridiculous." True, dogs can't do algebra. Nonetheless, they have humanity willingly picking up their poop, providing shelter for them and feeding them on a regular basis. We even throw people in jail for disrespecting them. Let me rephrase the previous sentence: without ever saying a word, dogs have shaped legal codes in their favor. We even let them sleep with us and our wives/husbands.
There are millions of animals on Earth, yet few of them have managed to charm their way into our bedrooms, let alone our beds. Even if we manage to lose our attachment to them, they go in to shelters that we pay for until someone else comes and gets them. Hell, we even pick them up off of the street to come live with us. Have you ever tried to persuade a homeless person to live with you? What about that squirrel you saw? You get the point.
Dogs and people go way back though. We have a longstanding alliance going back to the ice age. We were hunting things; they were hunting the same things, and we decided to team up. It was a negotiated, "you scratch my back, I'll scratch yours," type of relationship at the outset. Cats, however, had a rockier start with us. Cats just walked into ancient Egyptians' homes and were like, "We live here now. Deal with it." I imagine people were trying to get rid of cats at first (like, what would you do if a wild animal just rolled in to your house and starting killing things?).
Then, as we figured out that cats were killing pests, we let them stay around. This is the point where cats really showed off their ruling prowess. Even though they got their fill on eating pests and other things, we started to go out of our way to feed them; we started to use our hard-earned money to buy them accessories; I mean, we even created entire industries just to provide them with said accessories. Did cats appreciate the gestures? Nope, instead they decided to solidify their control over us by concocting a mind-controlling virus.
Humanity has domesticated many animals over our existence, but we domesticated most of those animals on our own terms. Conversely, dogs and cats chose us. They may not have been able to do math, but they knew we were up to big things. They invested in us when we were on the come-up, and they've seen our stock skyrocket over the millennia. Now, they're consuming our money, controlling our minds and making us pick up their shit on a regular basis. Nonetheless, we continue to love them more by the day. Therefore, dogs and cats rule the world, not because of their genius, but because of their ability to control the geniuses: us.
Side note: Wolves and wildcats (the ancestors of dogs and cats, respectively) are two gangster carnivores. The fact that they decided to team up with us is quite flattering and eye-opening as to how gangster we really are.