Its really only the developing world that is breeding like nuts. Which is ironic because they are also the poorest and least capable to handle it. Which means that the US ends up paying to feed the starving children.
This is ridiculous! The developing countries would be able to handle their population growth much better if they didnt had to export food and the like for your countries which require far more than what they need, so in the end the fault is also yours.
That's a fallacy. The primary problem with developing countries is culture. They have not yet gone through the cultural shift which accompanies medical progress and leads to a much lower birthrate. If you study the demographics carefully, the primary cause of strife in most developing nations is the birthrate, followed closely by the age-sex pyramid (mostly young people). This puts a huge strain on their economies and social systems, ultimately causing severe strife and frequently collapse. Food exports don't even begin to factor into it.
Unfortunately, in most developing nations children are still seen as something which makes your economic survival more likely (unlike developed nations, in which children are largely seen as a drain on economic resources and thus are not produced wholesale to support the family), which encourages large family size. That also leads to large numbers of youth, and ultimately large numbers of young adults for which the infrastructure is incapable of providing job. The extremely high unemployment rate causes social chaos.
At any rate, there is a direct correlation between the birthrate and the economic wellbeing of a country and its citizenry. Countries with birthrates around replacement (2.1) fare better than anyone else. Countries with birthrates lower than replacement are going to run into population problems (unless they allow their immigration levels to compensate), and countries with birthrates well above replacement have a whole host of problems already which are just being exacerbated.
Fortunately the good news is we're already starting to see the signs of the baby boom in developing nations - where death rate falls dramatically while birth rate remains high, causing a population spike. This is good news, because a dramatic decline in the death rate is always followed by a dramatic decline in the birth rate. So, we're starting to see the signs of a necessary population shift which will ultimately allow many of these nations to cope better than they have been.
For further reading on this sort of demography, look up "The Poverty Trap." It's a widely accepted demographic theory that is deeply nuanced. Unfortunately, it would take about 4 pages to adequately explain it here =)