(I'm going out of a limb here and consider that when people say babykilling they also mean abortion, for the purpose of the second part of the argument)
It is reasonable, considering only a species' own collective survival instinct, to think killing babies ia very bad thing. The whole comparison with animals is innocuous as human beings are intrinsically different than any other lifeform we know, and animals are not considered persons or actual members of our society, although they can have some rights. If killing some animal's baby is useful for our survival in one way or another, then it can be considered a good thing morally. Killing your own babies, however, is a pretty terrible thing in regards to how evolution and survival works in nature, since you're essentially preventing your genes from being passed on, which is terrible both on a collective and individual evolutionary level. As a consequence its not surprising at all that society has, in general, naturally opposed these actions. Aditionaly, while killing of babies does happen in nature, this does not essentially mean that it is a good thing for the species that practices it, as many animals have developed many terrible and self destructive habits through their evolution.
One could argue that babykilling can be considered morally good if it is done to preserve the life of a person that is already formed and is contributing to society and the species as a whole, which is why abortion is legal if its done solely to preserve the mother's own life (this is one of the few examples in which its possible to infer that the right to live is relative, not absolute, and that equality is also, legally, a relative concept, as the mother's life is considered more valuable than the baby's potential life, to the point that sacrificing that for the benefit of the mother's life is considered preferable to risking losing both the mother and the baby). This is why legislations across the world that criminalize abortion often have exceptions such as these. Another one is abortion in pregnancies that result from rape.
However, these exceptions are accepted because these are dire situations involving individual rights that, under a modern civilized outlook, are not considered reasonable to sacrifice in exchange for absolute preservation of a baby's right to live. This does not mean that, under normal circumstances, one could just sacrifice a baby's life to serve the whims of one person or another, because under normal circumstances such sacrifices are not considered legally reasonable. This is because the arguments against babykilling in general are not purely religious (unlike some people like to believe), but also sociological, bioethical and, of course, legal.