I don't believe in a god but that was such a flawed argument I'll defend it anyway.
First of all, god didn't create everything in his image. He created MAN in his image. Read genesis. Not dogs, not cows, man. Lets just pretend you weren't completely wrong from the get-go.
What you're saying is that if you kill something made in the image of something else, you are in fact also killing the model? What is this, voodoo? Your children are in the image of you and your women, correct? If I blast the brains out of your daughter with a shot gun, how is that killing you?
Why SHOULD we control everything? Because nothing else is. I am damn sure if a cow was capable of competing with human technology we would expect its rights - but it can't. You have already said that you have no religion so I am going to assume you trust science. Would you not agree that the strongest of a species outlives and out-fucks the weaker of the species? Let's take this to a social level. Those with the most charisma and brains become the leaders of nations. Since you're talking about animals getting the same rights as humans, they can be compared to us. You can quickly see they are inferior and have contributed (almost) nothing to society. That's why we own shit.