Of course Singer's well known for holding such positions that it may be morally permissible to kill hemophiliacs and babies born with down syndrome.
"Suppose a woman planning to have two children has one normal child, then gives birth to a haemophiliac child. The burden of caring for that child may make it impossible for her to cope with a third child; but if the disabled child were to die, she would have another... When the death of a disabled infant will lead to the birth of another infant with better prospects of a happy life, the total amount of happiness will be greater if the disabled infant is killed. The loss of happy life for the first infant is outweighed by the gainof a happier life for the second. Therefore, if killing the haemophiliac infant has no adverse effect on others, it would, according to the total view, be right to kill him." (Singer, Practical Ethics, p.186).Of course Singer doesn't know whether the "total amount of happiness will be greater if the disabled infant is killed." I, for one, would like to see the math. Do the utilitarian calculations. Show us all. Identify all the possible courses of action. For each course identify all the persons affected (this includes future ones), identify every happiness or unhappiness that will result for each person, assign the happiness and unhappiness a numerical value, calculate the net gain and loss for each person, sum it up and arrive at a grand total, then tell us the action with the highest utility. Oh, by the way, there's sub points for each of the above points. How do we rate pleasures to accomplish the first task? Do we need to look at intensity, duration, etc.?
Of course Singer may resort here to rule utilitarianism to escape these kinds of challenges. But it's not clear that this position, rather than lowering the amount of calculations needed to be done, actually raises the number of calculations. Rule utilitarianism only gives us rules of thumb. There are exceptions. And sometimes we want to know if we may be justified in breaking the rule in this or that instance. So we've done the calculation to determine the rule, and then did all the other ones I mentioned above. So sometimes rule utilitarianism means one more calculation than what you would do by doing the particular calculations. Other ways of getting around the calculation problem are to accept tradition, claiming the calculations have been done for thousands of years. But this begs the question. Utilitarianism seems like something new. There's no guarantee that the moral decisions the people in the ancient Near East, for example, used utilitarianism to arrive at their ethical decisions. For all we know they followed some kind of DCT. Another way is to assume a fixed human nature. But obviously Singer can't accept that since he depends on its falsity for his abortion and euthanasia arguments.
So, the first problem is that Singer can't justify his claim that killing one infant so another "healthy" one can live will result in more happiness. After all, what would have been the answer to Helen Keller’s mother? How about to the Menendez brother's parents? The latter was born affluent, with a lot of "prospects" for a "happy" life. The former, not a lot of "prospects".
What is even meant by "prospects" for "happiness," anyway? Singer talks of the "clouded prospects" of down syndrome kids on page 213 of his book Rethinking Life and Death. And how are their prospects clouded? The may not be capable, says Singer, "to play the guitar, to develop an appreciation of science fiction, to learn a foreign language, to chat with us about the latest Woody Allen movie, or to be a respectable athlete, basketballer or tennis player."
And atheists lay all the blame for discrimination at the feet of "religion," but I digress... So, we can justifiably kill our down syndrome children because they can't enjoy a Woody Allen flick. One might claim that these movies increase suffering, but I digress... A question might be, who died and made Singer the "prospect granting fairy" anyway? And apparently participating in the Special Olympics is not being a "respectable athlete." But what if we included "respectable Special Olympian" on the list? If we add that, and then add that enjoying Allen flicks increases suffering, can we kill Singer? But I digress...
This all seems an odd criteria by which to establish what makes someone's human life valuable. But it fits with Singer's "having a past and future" criteria of what makes it "especially" wrong to murder such a person. This is similar to James Rachels' well-known distinction between biological and biographical life (it's beyond the scope of this post to interact with Rachels' distinction directly. One can read critiques of his view in Moral Choices, Scott Rae, pp. 191-196; also see J.P. Moreland's James Rachels and the Active Euthanasia Debate, in Clark and Rakestraw eds. Readings in Christian Ethics, vol. 2, pp. 102-108).
To see Singer's "past and future" criteria for what makes a killing "especially wrong" (it is important to note that Singer does admit that euthanasia and abortions are instances of killing), he writes,
Killing an autonomous being against that being's will is the most drastic possible violation of autonomy, and this makes it more seriously wrong than the killing of a sentient being not capable of autonomy.Why is it "especially wrong" to kill these beings? Because there are other beings that it is wrong to kill. Wrong simpliciter? Perhaps, wrong Lite? These include those beings that can "feel pleasure and pain." Animals fall into this category, but not plants. (Not even ones that grow better when you play Vivaldi around them?) Of course it is not clear how Singer argues for the above. Apparently this kind of "pleasure and pain" is distinguishable from "enjoying science fiction" and "suffering through Annie Hall." It must mean something crass. Feeling pain and pleasure through one of your sense organs. And how he makes it fit in with his physicalism is another question. What is "pain or pleasure" on physicalist assumptions? And why think what we feel when stabbed with a knife is anything like what an animal feels?
Rachels focuses on whether the being can live a biographical, rather than a merely biological, life, which is similar to the emphasis given by Singer to the ability to see oneself as having a past and a future. To kill such a being, unless at the being's request, thwarts the preferences for the future that the being may have, and this makes the killing wrong in a way that is additional to any wrong that may be incurred by the killing of a sentient being unable to form any preferences for the future.
The effect of these arguments is to distinguish a class of beings whom it is especially wrong to kill.
These questions aside, we can note that Singer is arguing that "seeing yourself as having a past and a future" is what makes killing you wrong in specie, feeling pain and pleasure in a crass way is what makes killing you wrong Lite.
I propose to offer a thought experiment that gets around all these criteria, yet where it would still seem wrong in specie to kill the being.
First, note that you must see yourself as having a past and future. You don't actually need an actual past because, presumably, it would be wrong to kill someone who could play the guitar, had an appreciation of science fiction, learned a foreign language, could chat with us about the latest Woody Allen movie, and was a respectable athlete, basketballer or tennis player, who, like the rest of the universe, "popped" into existence, with all our memories included, 5 minutes ago. This person, call him Mozart in excelsis, would "see" himself as having a past, though he actually would't have one.
So, let's assume Mozart in excelsis gets hit by rays emanating from Alpha Centauri that cause him to blank out when he thinks about his past. Mozart in excelsis can still do all of those wonderful things, yet he doesn't "see himself" as having a past.
 So, Mozart in excelsis does not see himself as having a past.
For now we'll let slide that Singer constructs his criteria as a conjunction, so if one conjunct is false, the entire conjunction is false. We can move on to the future.
Say that the evil Alpha Centaurians hate earth with a passion. So, they manipulate asteroids and send hundreds of them hurling towards earth. The president is informed by NASA and goes on the news and lets the planet know that we have roughly 5 days to live, then we are guaranteed to die. We have no future. We cannot see ourselves as having one.
 Mozart in excelsis does not see himself as having a future.
Now, can I kill Mozart in excelsis and have it not be "especially wrong?" I don't see why not. On Singer's terms, at least. This is bad enough, but Singer would still say that it would be wrong Lite to kill Mozart in excelsis. So, let's add another proposition:
 Mozart in excelsis develops CIPA (congenital insensitivity to pain with anhidrosis) and so cannot feel pain or pleasure in a crass way.
Apparently , , and  taken together mean that it's not wrong, at all, to kill Mozart in excelsis for no reason whatsoever.
So, we could kill someone who could play the guitar, had an appreciation of science fiction, learned a foreign language, could chat with us about the latest Woody Allen movie, and was a respectable athlete, basketballer or tennis player and it not be wrong at all.
Maybe Singer could come back with some other criteria. For example, he also, in other places, talks about how others (like parents) would feel about the death of their disabled child. He says we need to take their feelings into account to. But all we need to do is adjust our thought experiment accordingly. We could then kill Singer's paradigmatic "person" and have it not be wrong at all. But this was the very person, with the very characteristics (playing guitar (presumably not Metallica, though), enjoying sci-fi films, etc.), Singer put forth as the paradigmatic "off-limits" person!
Singer's problem lies in the fact that he denies any human nature, or substance, that grounds and is a necessary pre-condition for having, or potentially having, any of his particular qualitative hedonic characteristics. He denies, for example, that humans are image bearers of God, by nature. That nature grants prima facie sanctity to human life. The Christian ethic doesn't succumb to such absurdities. But, we would agree with this conditional (written in a short-hand way, i.e., qualifications omited): If morality, then God. No God. No morality.