The comparison that Peter Singer makes between racism and sexism, on the one hand, and so-called 'discrimination' against non-human animals, on the other, is ill-founded. Racists and sexists discriminate against people who are fundamentally equal. So called 'speciesists' assert something that is factually true: that there is a fundamental moral distinction between humans and other animals.
Humans are clearly animals, evolved beings with evolved minds. But humans are also distinct from all other animals by virtue of being subjects: rational, autonomous, moral beings who are, in Kant's phrase, self-willing. Equal rights derive not from a common capacity to suffer but from a universal ability to act as moral agents, capable of distinguishing between right and wrong, acting on that distinction and being held accountable for such actions.
It is true that children and the severely mentally disabled may be neither rational nor autonomous. But children normally grow up to be full members of the moral community. And the severely mentally disabled are of the kind that, but for an accident of nature, would have been rational, autonomous beings. They are of the kind whose normal instance is a moral being. Non-human animals are not. They do not have, never have had, and never will have, the potential to belong to a moral community. That is why we must treat humans as ends but can treat animals as means - for instance to farm them for food or experiment on them to develop scientific knowledge and medical treatments.
I believe that in certain circumstances infants born with painful, terminal conditions should be allowed to die. However, the implication of Peter Singer's argument is that it is morally acceptable to kill any child who is not cognitively more advanced than a non-human animal. But why should the cognitive ability of non-human animals provide the benchmark for determining the moral principles by which we decide whether human infants should live or die?
Humanity is not invested in a single person, but is a collective label, describing our existence as social beings. It derives not from our individual selves but from our membership of the human collective. We only exist in relation to others, and it is only in relation to others that we make sense of every individual's humanity. A severely disabled person is human because the notion of humanity would become meaningless if we did not extend it to the severely disabled too.
Peter Singer suggests that he provides 'a critique of long-standing prejudices against those beyond boundaries'. But the meaning of boundaries depends on context. From an evolutionary viewpoint Homo sapiens is just another animal. From a moral viewpoint, however, there is a profound distinction between humans and other animals. The fundamental point with Peter Singer's argument is the same with any utilitarian philosophy: it may be logical in some abstract way, but it is not rational within the framework of actually-lived human lives. A philosophy which deems it immoral to cage a chicken but acceptable to kill a child makes little sense given the kinds of beings that humans are and the kinds of lives we aspire to live.