Doesn't the Bible say that humans have
dominion over the animals?
Yes, the Bible states this in the story of Genesis after God
creates Adam and Eve and the Garden of Eden. Although I myself
believe in the theory of evolution, there are some vegetarians
and animal rights activists who do believe in the literal
interpretation of the Bible. These individuals would point out
that according to the literal interpretation of Genesis, no
animal ever died in the Garden of Eden. Therefore, in the Garden
of Eden, Adam and Eve and all the animals were vegetarians.
In this context, the phrase "dominion over the animals" could not have referred to killing and eating them. Many would argue that "dominion" is more accurately interpreted as "stewardship" rather than tyranny. Furthermore, since the Garden of Eden represents the highest ethical ideal, some people who believe in the literal interpretation of the Bible interpret this to mean that vegetarianism is the highest ethical ideal.
Follow up questions:
Doesn't the Bible specifically state that it is ok to kill animals for food?
If God did not want us to eat meat, then why did he place animals on the Earth?
Don't only human beings have a soul?