I believe humans and animals are equal and we do not have the right to take their lives.
A slightly better reason than the knee-jerk "poor little bunny rabbit" school, but I don't think it really holds water.
You have an unstated assumption:
If humans and animals are "equal" in some respect, then the standards should be the same.
That is debatable in its own right, but I'll stick with it.
We don't have the right to take their lives.
Is this for any purpose, or just for food? If only for food, why should that differ?
Proceeding to the main argument...
Since we are "equal", then presumably animals do not have the right to take other animal's lives. This would make all carnivores and omnivores immoral. Do you propose to convince them of the error of their ways? Punish them? Eliminate them?
If you could humanely eliminate all the natural meat eaters, what do you propose to do about the ever-expanding populations of the herbivores? Should the remaining (vegetarian) human population move over and allow them to graze out all "our" farmland? Should we cull them (oops, no killing, my bad), or keep them out somehow so they starve...?
We have evolved as omnivores. That gives us as much "right" to eat meat as any other omnivore.
I think there are strong reasons to eat a reduced-meat diet from both a health and an environmental perspective, but you'll need a very good counter-argument before I buy into animal rights as a valid justification.