Fewer babies survive when there are environmental stresses. Each woman needs to have 2.1 children just to break even population-wise. Currently, much of the Western world is below this replacement rate. By 2050, if things don't turn around, the population will plateau and then begin declining. You seem to ignore reality in your calculations.
Show me evidence that man used birth control for 300,000 years and the argument about western birthrates might have bearings. Otherwise, current birthrate is completely irrelevant.