As well written and funny as the article is it still finds itself in a tunnel vision scenario because if the population is rising continuously and no one wants to have kids anymore then where are all these extra kids coming from?
The developing world. Lack of birth control + poverty + lower cost of raising children has our population exploding in all the places that haven't developed yet.
You forgot the most important point, security when your old, if you have 10 children's the "burden" to provide money/time to the parents is smaller per child.
If the state is not providing "insurance" the family has to.
It depends on the culture, I guess - AFAIK the birth rate in western countries is decreasing.
On the other hand, the taxi drivers I remember talking to about children, had all a certain (non-western) background, and they had (as far as I remember) 2, 4, 3, 8 children, respectively.
Aside from the apt Yogi Berra reference, a lot of kids are made by "accident" by people who didn't "want" to but accept their fate when it's "happened". Oopsie!