Since my daughter (TheGirl) was born, I have wondered a similar thing. More particularly, I've wondered how it is that mankind has survived this long when newborns are so very fragile and so very irritating. (Oh give me a break. Kids are great, but babies? They're fucking pains in the ass...) As infants, each of my kids has pushed me to within a hair of insanity. Certainly, caveman babies behaved similarly. And presumably, cavemen were even less restrained than I am. So why weren't all the babies killed back then?
All I can think of is that the real torture of screaming infants is staying there and dealing with them. Society insists that we not abandon our kids, even for a little while (say, long enough to get a good night's sleep). Maybe the cavemen just took off when they got crazy... headed out to the nearest proto-tavern, and ate fermented berries until the sun came up.
NO? OK, an alternte theroy... maybe babies were being dropped over cliffs, and that's the reason for the extreme population bottleneck that DNA analyses see signs of about 70,000 years ago. In this theory, we'd have to have been about to exterminate our species via infanticide when whatever is is that kept me from chucking the kids out into the wintry night developed for the first time in cavemen... and mankind blossomed.
[Ed. note - by "cavemen" I am referring to early humans, either anatomically modern, or nearly so. Yes, I know that the term technicaly refers to Neanderthals, and I know that there's no evidence surviving humans are related to Neanderthals. So give me a break, 'K?]