Natural here is not referring to crunchy granola, but in the philosophical definition: according to the nature of the thing. The secular Western civilization has largely moved away from philosophies of teleology (fancy way of saying that things have purposes and meanings, from which they derive their nature). Thus, most people perceive human fertility not innately much differently than the sort of complex systems in a car or a computer. One can customize, experiment and make changes at will!
But Catholicism says that human sexuality is a completely intertwined whole. Marriage, intimacy and babies are not really different subjects. Rather they are ONE subject viewed from different angles. In the same way that a precious gem has facets, those facets are not divisible from the entirety of the jewel without BREAKING the jewel.
Contraception is a physical manifestation of a lie that says “sexual intimacy has nothing to do with babies unless we WILL it to.” That mindset profoundly damages the human person and the marital relationship. When a couple has a serious need to avoid pregnancy and they use NFP for that, their intimate life never stops respecting the link between sex and babies because of that excruciating period of denial that is required during fertile times. That hardship literally keeps things fully human.
As to population, it’s a big myth that humans will breed explosively, indefinitely without contraception. The science of demography has pretty conclusively found that population growth rates only become large during the transition time between pre-industrial rural societies and industrialized urban society. As far back as the late 1800’s third generation middle class urbanites already had an average of just over 2 kids per couple: bare replacement rate. By contrast, mature industrial societies today in which contraception is widespread, cheap and respectable have only 1.7 kids or so per woman: BELOW replacement rate! Google CIA World Factbook Total Fertility Rate and have a look for yourself. Contraception so totally alters human views on sexuality that there is not ONE first world nation on earth in which contraception is cheap, widely available and socially respectable that has enough babies to sustain it’s own population anymore. Not one! Remaining global population growth is ONLY in the third world and even those rates are coming down pretty fast.
And finally, you still seem to think NFP is Rhythm. It’s not. Rhythm was based only on calendar days. NFP methods are symptoms based. Humans are mammals and mammals all display detectable symptoms of fertility. It’s neither magical, nor rocket science either.