Who is to say that our lives are more important than the lives of animals?

Okay, granted... we are at the top of the food chain. Bravo. Most of us being meat-eaters, we've probably eaten a good few cows, pigs etc etc But whenever you observe an animal's behaviour (or even an insect's) you can see how responsive it is to pain. You touch a spider and adrenaline will ignite through it's body, making it sprint away from danger. Animals look after their offspring and make sure they are fed. So how do we honestly know that are lives are more important and that animals don't matter?