Technically, this is not true. Our ethical conduct is rooted in our social codes. Certain societies hold certain animals in higher standing than others. This plays out around the globe.
I do not support an anthropocentric view of our species as the center of all life on this planet, but I disagree with the notion that all animals have some intrinsic right to life. Let's remember that most life on this planet is sustained through death, and that animals are excellent practitioners of death. The animals that are societally held in high esteem are the ones that evolved to work well and serve the humans within that ecosystem. Which is why we respect dogs, horses, and cats, etc.
The reason the cow is sacred in India is fundamentally because most of India cooks with dried cow manure. If you took away the random cows hanging out in the slums (by eating them), no one would be able to boil water or cook rice. An animal is respected only in so much as we are in awe of it (dolphins, whales, etc) or that it serves a purpose (horses, dogs, cats, pets).
I'm not saying this is an ethical view--and I for one do not share it--but let's not play fancy games and skip around the facts here. If we elevate every living thing to the same status, then no more swatting mosquitos or killing rats. You know why we kill rats and mosquitos? Because they carry diseases that kill us in droves.
