lets just say for argument sake, that humankind or civilization has been on Earth for 2000 some years. You would have thought with the advances in technology we would have all ready realized the scenario that you present.
I presented nothing of my own Philly, but let's say it were.
The fallacy is that all societies have not advanced technologically at the same rate. They haven't because that particular development depended on the Protestant Reformation which occurred only in Europe. Even within Europe, different cultural groups demonstrate different attainment levels due to time exposed to better health care and education as well as acceptance into that society.
Now that technology and communication have reached unprecedented levels in those European and European influenced societies, mass education has become a real possibility for the third world. Health care has lagged behind as it is (on the actual care giving level) far less profit driven and far more tech dependent. Also, it has lagged because of the political/cultural/economic lag in the third world. Thus time has a different meaning depending on where you are.
In those that have gotten the education and health care, the fertility rates have fallen off. They are running 1.3-1.8. To sustain, the rates must be 1.8-2.0 and to grow, >2.3.