Not true. Human populations were lowered during the Black Death, for example.
the “birthrate of man has consistently been higher” is a totally false claim as demonstrated by Erope’s loss of about one-thrid of its entire population during the Black Death. In order for Europe’s population to shrink by a thrid, it is patently obvious the death rate exceeded the cirth rate in the years of this depopulation o feurope. The same is true of the plagues in Greece, China, and the New World. Worldwide human populations have suffered net losses instead of gains at many periods of human history, which means the assumption of only gains has no basis in reality and is a recklessly false claim.