I think you're intentionally ignoring the repeated and well-substantiated argument that growth rates have not stayed the same for thousands of years. Modern food production and medicine have dramatically increased our life span, fertility, and survival to sexual maturity. Human population density has reached plateaus at many points, where further growth was only possible through technological advances - from hunting and gathering to traditional agriculture, and from there to industrial agriculture, for example.
To ignore the recent and unique advances that have pushed the growth rate well above historical averages, and simply extrapolate at will, is ludicrous. We know what changed, and how, and when, and we know the results.
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