I recently finished Babies and Beasts: The Argument from Marginal Cases by Daniel Dombrowski. The entire book is dedicated to the debate surrounding the AMC. Unless you're excessively interested in the topic, as I am, I don't recommend that you read it. It's not very interesting.
By which I mean no disrespect to the author, he handles the material fine and writes quite clearly. But in truth, there's really not a lot to say on the matter. Though a lot of writers have opposed the AMC, most replies to it are clearly ad hoc or question-begging. A lot of the book is repeating the same few objections and fallacies over and over, with slightly different phrasing and context. I've never before read a book on a single debate and thought one side was so obviously correct. (And this is not bias on my part--remember that I was initially convinced of animal rights by this very argument.)
There is one reply, however, that might appeal to someone who does not share some of my meta-ethical views. This I will call the Sentimentalist Reply.
Let's review the argument. Most simply, it tells us:
1. There are some members of the human species who share mental capabilities on a par with non-human animals, such as babies and some cognitively disabled humans.
2. These humans (i.e. the "marginal cases") are entitled to the basic human rights that we accord every normally functioning human.
3. Species membership is not a morally relevant quality.
4. We ought to accord nonhuman animals the same rights we accord to all humans.
There are two versions of the Sentimentalist reply, which deny either 2 or 3. If you deny 2, you can say that "marginal cases" are not entitled to rights, but we just grant rights to them because we have a non-rational emotional response to them (some people might claim that no one has any rights, and all morality is non-rational responses.) But this is false.
If it were true that babies or the cognitively disabled had no rights, there would be no objection to abusing them. If my neighbor enjoyed killing babies, and I don't, my disagreement would be as significant as our disagreement in movie choices. I don't enjoy killing babies, but he does, which is alright, because it's also fine if he likes watching romantic comedies, even though I don't. Morality is not like this.
Some people might just say that babies and the cognitively disabled have no rights, and we have no reason to treat them well. I feel no need to talk to such people.
A sentimentalist could also deny premise 3. They could say that we do have an emotional response to "marginal" human cases, and this is what makes species membership morally significant. But this reply is really little better than the first. Not everyone necessarily has this emotional reaction-- does this mean it's okay for some people, but not all, to fail to respect the rights of some individuals? On the other hand, some people (myself included) have strong emotional reactions to the lives of animals--does this mean we should accord them rights?
To me, it seems obvious that asking how we feel is the wrong question. Our emotional reactions are important, but what's important is that we have good reasons for them. If everyone in the world had the same sentimental regard for couch cushions as (most) people have for babies, that wouldn't mean couch cushions are actually as morally important as babies. Everyone would be making a mistake.
The right question to ask is this: do we have good reason to have strong emotional reactions towards others? Which others, and which kinds of reactions? The AMC helps us, in part, answer these questions.