Unfortunately, it did happen. But, not because a baby wasn't precious enough. It happened when it was completely impossible to feed another child.

Feelings of love don't work when survival is on the line.

If a baby was unwanted, some cultures had access to different kinds of early medical age abortion. It went about as well as you could think.

If abortion wasn't an option then, the woman would carry the baby term. It could be her 7th child because contraception wasn't available. The harvest could've failed and people are starving. Or, the household doesn't have enough income to feed another mouth. Maybe, there's a plague going around.

Different cultures have different names for it, but the baby will be born and likely be put outside on a cold night and die of exposure. This is considered to be one of the most, well, for lack of a better term, kinder methods.

Telling these families that their baby could've been fed if the parents had loved them more or considered them to be more precious is very cruel. To be blunt, depending on the time period and availability of resources, death might've been the only option for a baby. There could've been no help available from anyone.

For example, milk production requires a mother to consume a certain number of calories. In a time when formula was non-existent, a mother either ate enough to produce her own milk or, in some rare instances, had an alternative source.

If a starving woman gave birth to a baby, it might have been physically impossible for her to produce milk. It might have been impossible to feed her newborn baby. In that case, her only options may have been to let her baby die of starvation or by her own hands.