The contemporary philosopher, Peter Singer, is not the only modern thinker who thinks ‘the handicapped baby should die’. Eugenics is not dead, it is just in hiding. Singer is just more outspoken than most.

But he, like other eugenicists, is guilty of a fallacy. His views may seem obviously wicked to some of us; but to many others they are quite tempting. Yet they are also deeply illogical – as I will attempt to show – and it is logic by which philosophers like Singer must live or die.
To begin with, let us acknowledge, even if we know that we  disagree with the eugenicist, that their  arguments do build on some kind of distorted truth.
Humanity is varied (as it should be) and, of course, part of that variability means that there are some of us who are weaker than others. [Although the concept of weakness is quite ambiguous concept, but we’ll leave that for another day.] This weakness, for example, might mean that I might need help to eat or to thrive; and this help can be treated as a cost – not just a financial cost – but as a cost in the lives of others. 
The eugenicist then demands that we put aside compassion, sympathy or love and instead we judge ‘honestly’ and examine the ‘burden’ that love or morality seems to demand: all the feeding, the caring, or the helping. At some point, they argue, we must recognise that this burden just becomes ‘unreasonable.’ And, of course, there is a genuine temptation here. Most of us might resent the care that we must take of others – all of us can imagine something else that we might do that would be more fun, pleasurable, relaxing, creative, productive etc. [Here we can each choose our own utilitarian poison.]
But how can there be an end to this. Each time we destroy the weakest a new weakest must emerge. Those who were second from last will now become last. There will always be someone with less, who needs more, it is a fundamental aspect of the human condition. The eugenic knife must keep on cutting – once we’ve decided that we are at liberty to destroy the weak we will find new people who are weak – and who must therefore be destroyed.
There can be no end to the destruction. And as the process destruction begins there must therefore appear two classes, those who destroy and those to be destroyed. We may feel that we will not belong to either class, but ultimately we must choose – there is only the illusion of a middle ground. If we are silent while the destruction goes on then we are complicit with destruction. If we resist then we stand with those who they wish to destroy.
Eugenics always opens this gulf within humanity – it is profoundly inhuman because it forgets that diversity and weakness is of our very essence. But it is profoundly illogical because it forgets that eugenics changes everything, for all of us. The eugenicist argues as if the act of genocide is merely some neutral act of science. But always there will be those who wield the knife, inject the toxin or turn on the gas. We must become killer or victim. And as the victims pile up the killers must turn on each other. Eugenics is pragmatically self-contradictory – it cannot be sustained (which is not to say it cannot happen – it is happening now).
Eugenics is a particularly tempting philosophy for those who are powerful or wish to be amongst the powerful. In the nineteenth century, as Arendt argued, it was a critical element in the thinking of al the competing elites – liberals, progressives, imperialists and racists:

Darwinism met with such overwhelming success because it provided, on the basis of inheritance, the ideological weapons for race as well as class rule and could be used for, as well as against, race discrimination. Politically speaking, Darwinism as such was neutral, and it has led, indeed, to all kinds of pacifism and cosmopolitanism as well as to the sharpest forms of imperialistic ideologies. In the seventies and eighties of the last century, Darwinism was still almost exclusively in the hands of the utilitarian anti-colonial party in England. And the first philosopher of evolution, Herbert Spencer, who treated sociology as part of biology, believed natural selection to benefit the evolution of mankind and to result in everlasting peace. For political discussion, Darwinism offered two important concepts: the struggle for existence with optimistic assertion of the necessary and automatic “survival of the fittest,” and the indefinite possibilities which seemed to lie in the evolution of man out of animal life and which started the new “science” of eugenics. 

The doctrine of the necessary survival of the fittest, with its implication that the top layers in society eventually are the “fittest,” dies as the conquest doctrine had died, namely, at the moment when the ruling classes in England or the English domination in colonial possessions were no longer absolutely secure, and when it became highly doubtful whether those who were the “fittest” today would still be the fittest tomorrow. The other part of Darwinism, the genealogy of man from animal life, unfortunately survived. Eugenics promised to overcome the troublesome uncertainties of the survival doctrine according to which it was impossible either to predict who would turn out to be the the fittest or to provide the means for the nations to develop everlasting fitness. This possible consequence of applied eugenics was stressed in Germany in the twenties as a reaction to Spengler’s Decline of the West. The process of selection had only to be changed from a natural necessity which worked behind the backs of men into an “artificial,” consciously applied physical tool. Bestiality had always been inherent in eugenics, and Ernst Haeckel’s early remark [1904] that mercy-death would save “useless expenses for family and state” is quite characteristic. Finally the last disciples of Darwinism in Germany decided to leave the field of scientific research altogether, to forget about the search for the missing link between man and ape, and started instead their practical efforts to change man into what the Darwinists thought an ape is.

Hannah Arendt from The Origins of Totalitarianism 

Today we have our own ‘neoliberal’ version of eugenics. ‘Let the market do the work of the eugenicist. Let those who are unworthy fall aside. Greed is natural and good. We are powerful, rich and strong because we are the best. We should survive and thrive, they should fail.’
This road to Hell has been trod before. The fact that it is all illogical nonsense does not stop it from growing in strength. Its strength is rooted, not in truth, but in fear and in our natural desire not to find ourselves on the losing side – the side of the weak. 
The only thing that will stop it before it destroys everything is that either when the weak themselves resist or that those who have not yet been marked out as weak choose to stand beside them. 
The trial lies before us now, but we close our eyes and hope it will go away of its own accord. This never works.