I have been told that the primary reason is that killing animals is morally wrong, not that it is in any way comparable to murder. I have never met an vegetarian so extreme to tell me that animals (we eat) are people.
Whether killing animals is comparable to murder is a different question than whether animals are people.
Peter Singer argues against the species-ist argument that they're incomparable. Or that killing any human is worse than killing any (or even all) animals, i.e. he argues that for some human,animal pairs killing the human is less-worse than killing the animal.
> Q. I’ve read that you think humans and animals are equal. Do you really believe that a human being is no more valuable than an animal?
> A. I argued in the opening chapter of Animal Liberation that humans and animals are equal in the sense that the fact that a being is human does not mean that we should give the interests of that being preference over the similar interests of other beings. That would be speciesism, and wrong for the same reasons that racism and sexism are wrong. Pain is equally bad, if it is felt by a human being or a mouse. We should treat beings as individuals, rather than as members of a species. But that doesn’t mean that all individuals are equally valuable – see my answer to the next question for more details.
When someone says murder most people think 'subset of killing humans' — that's how people come into play. I don't ink you are really referring to a mainstream vegetarian argument there.
There is even vast common ground between meat eaters and vegetarians. Most people agree that killing primates it morally clearly wrong.
Singer's is a utilitarian framework for arguments about vegetarianism and other animal-rights issues; not an argument for vegetarianism, per se. Animal Liberation is a great, mind-opening read.
> Most people agree that killing primates it morally clearly wrong.
Roughly, you're probably right: killing primates is generally wrong. But it's not always, clearly wrong: killing a primate that's about to kill you, killing primates that are consistently killing other primates, killing one primate to save a hundred other primates, etc., etc. Singer's framework gives us a way to reason-through cases where there isn't consensus.
Quite a few quote the circumstances under which meat is 'produced' as another primary reason, i.e. not the killing of animals for food per se, but the conditions created by the industrialized process optimized for efficiency in killing.