People are nutjobs.
Reasons being:
Firstly--an average person in a first world country has a higher effect on global warming than an entire village in, let's say, rural Africa, and let's not even start on
what the very few super rich do to our environment.
Secondly--Populations in first world countries are actually declining, or expected to decline, for the most part. Way too lazy to find the information on this again, but if you want to you can go
here and check population growth rates in the last ten years. You should also compare ones which seem to rise with immigration rates (like the US had a huge pop. growth rate between 2008 and 2009, but it also perfectly corresponds with a net migration rate increase). And because I could find it:
Japan's projected population 'growth' numbers over the next 100 years. From what I remember most of the first world looks like this, as well.
Thirdly--Even in countries where this isn't the case (the US is one, I believe), our populations growths are far lower than third world countries, which still require more children to 'work the farm' as it were.
Basically, putting a cap of one child per family globally, would do almost nothing to stop planetary climate change. It might help stop 'over population' but that's a set of words that most people who use it don't actually understand. The real result would just be causing a bunch of people in third world countries to starve EVEN HARDER.
Not to mention it hasn't even worked worth shit in China, where population is still estimated to be increasing.