The historical Greeks considered the practice of adult and child sacrifice barbarous. However, exposure of newborns was widely practiced in ancient Greece. In Greece the decision to expose a child was typically the father's, although in Sparta the decision was made by a group of elders. Exposure was the preferred method of disposal, as that act in itself was not murder; moreover, the exposed child technically had a chance of being rescued by the gods or any passersby.This very situation was a recurring motif in Greek mythology.
If the husband accepted it, it would live, but if he refused it, it would die. Babies would often be rejected if they were illegitimate, unhealthy or deformed, the wrong sex (female for example), or too great a burden on the family. These babies would not be directly killed, but put in a clay pot or jar and deserted outside the front door or on the roadway. In ancient Greek religion, this practice took the responsibility away from the parents because the child would die of natural causes, for example hunger, asphyxiation or exposure to the elements.
In some periods of Roman history it was traditional for a newborn to be brought to the pater familias, the family patriarch, who would then decide whether the child was to be kept and raised, or left to die by exposure. The Twelve Tables of Roman law obliged him to put to death a child that was visibly deformed. The concurrent practices of slavery and infanticide contributed to the "background noise" of the crises during the Republic.
In the High Middle Ages, abandoning unwanted children finally eclipsed infanticide. Unwanted children were left at the door of church or abbey, and the clergy was assumed to take care of their upbringing. This practice also gave rise to the first orphanages.
In Kamchatka, babies were killed and thrown to the dogs. American explorer George Kennan noted that among the Koryaks, a Mongoloid people of north-eastern Siberia, infanticide was still common in the 19th century. One of the twins was always sacrificed.
Since feudal Japan the common slang for infanticide was "mabiki" (間引き) which means to pull plants from an overcrowded garden. A typical method in Japan was smothering through wet paper on the baby's mouth and nose. Mabiki persisted in the 19th century and early 20th century.
I can fully understand you not wanting to put your kid to death, it's a severe cultural taboo nowadays. Obviously part of a brave new world means we will have different cultural practices and it sounds to me like we won't be capable of supporting defectives until the world is far less populated.
The biggest voices against infanticide in the past were Christianity, Judaism, and Islam. I'm under the impression that most can agree that none of those viewpoints lead to a healthy society in the long term.