For most of human history -- and until just a few generations ago -- taking care of one's parents was every adult's duty. And adults had children, among other reasons, for their own support in their old age.
Old habits die hard. With infant mortality down in the late 19th and early 20th centuries, "have a lot of children so that at least some survive to take care of you in the future" made for explosive population growth.
Fast forward to 1970-present, and TFR has collapsed in every industrial country. The cause can't be put down to any one thing in particular, but two big reasons are (1) the modern welfare state, and (2) the fact that adults are expected to live lives wholly independent of their parents. (And so often seem to begrudge their parents.)
Strong family ties are a good thing. If not in every case, children should take care of their parents as a general rule. The collapse of this notion, /w woe-is-me bellyaching and snide commentary from the NYT, is leading modern societies to a very dark place.