What's wrong with the "marginal humans" argument against meat-eating?

Ayn Rand (in agreement with Aristotle) defined man as the rational animal -- meaning that man's essential quality is that he possesses the faculty of reason, while other animals do not. In debates about vegetarianism and animal rights, many advocates of eating meat try to use this distinction to justify raising animals to be killed and eaten. They say that animals have no rights because they are not rational, and hence, we can do whatever we please with them. Advocates of animals rights, however, reject this claim via the "marginal humans" argument. They observe that human infants lack the faculty of reason, and hence, we should not use that as the relevant moral criterion. What is wrong with this argument? Does the meat-eating viewpoint conflate potential with actual rationality, in that the infant seems potentially but not actually capable of reason? Is eating animals the same as eating human infants?