To cut a very long story short, and to step carefully around the plethora of associated conspiracy theories, the Guidestones set up a vision for world government that just happens to necessitate the extermination of ninety percent of the human race, not to mention the end of any kind of national self-determination. In one form or another, "human population control" is becoming very fashionable in "green" circles, although it's usually expressed in a more moderate form, even if the logical implications are extreme. In other words, the difference between Sir David Attenborough's views on the subject and those of someone much more extreme, such as Jonathan Porrit, really boil down to the percentage of the population that needs to go, rather than the principle. It is taken for granted by all those involved in this kind of debate, that "the sacredness of human life" is at best an obsolete religious concept, and at worst a form of arrogance that values human lives above those of animals, or even biospheres. Medawar seeks, therefore, to tackle this one on its own terms and not with moral or theological arguments that might be better made by others.
Population Control, in the minds, and the hands, of those using the term today, means or implies genocide. They are not talking about limiting population growth or movement, they are talking about either massive, or in some cases, nearly total, elimination of populations. The "rational" justification for this is to claim that humanity is causing mass extinction events, and therefore the whole race is "guilty" or at least a deadly threat to the global biosphere, and this requires its removal or neutralization.
Obviously, the removal of 90% of the human race is an extinction event in itself. Probably, however, it wouldn't be possible to neatly remove 90% and leave 10% intact, viable and thriving, so the likelihood is that any attempt to realize the 90% cut in our numbers demanded by the stones, would take the human race perilously close to complete extinction. Currently, and this is the nub of the pro-genocide argument, the human race dominates every single habit in the world. Well, that makes us the dominant species throughout the biosphere.
If one looks at actual mass extinction events throughout the world, and throughout time, there are two mechanisms which recur time and time again. One is the sudden and massive proliferation of a pest species, which is what the Guidestoners believe humans are. "A cancer on the Earth". The other is the precipitate removal of a dominant species, which is not only a huge ecological wrench in itself, but also generally allows the sudden proliferation of another species that proceeds to wipe out all kinds of others. In effect, knocking out one thing makes space for another and ecological balance may not be restored for eons.
So, those looking for the cause of all the dinosaurs dying out, keep looking for huge events that would wipe the Earth clean of all life; except for some plants, insects and a few, Temrec-like, mammals. But all that's required for a mass extinction event is something that kills a few dominant or core species, or groups of species, and creates a vacuum into which something else multiplies, probably to its own ultimate destruction. If one or two types of creature, that were very dominant, were obliterated over a comparatively short period, there would follow a very long period of ecological instability and constant change and interaction, during which practically everything else either adapts, not once, but constantly as everything else changes, or dies out. Removing a dominant species spells long-term doom for thousands of others.
Humans are now THE dominant species, core to every eco-system, whether the Guidestoners like it or not. Our wholesale removal will destroy, not just many species, but probably whole categories of life. A "New World Order" might in the end prove not to be a profound political or humanitarian change, but a taxonomic one, in which the whole basis and pattern of life on Earth became unrecognizable. "New World Phyla" might be more apposite.
There are problems and dangers with the scale and nature of human activity as it is now. But it is wiser, indeed imperative, to address this by the gentle, and consensual, adaptation of human activity, rather than by the ruthless removal of human population.
Political, rather than truly scientific, "ecologists" tell us that we live in a small world of finite and dwindling resources. But cosmologists tell us that we live in an expanding universe. It is physically impossible for the human race, or any other species, to expand so fast that it outruns the space available to it in cosmological terms.
Intellectually, too, we have at least the potential to live in an expanding universe, where our knowledge of what the possibilities and solutions are, grows faster than the problems we make for ourselves, or for others. But that requires us to see knowledge and wisdom as living things, ever changing, ever growing, never needing to mean exactly the same thing to every beholder, not suffering from different usage and interpretations. If we carve our "wisdom" on granite monuments, we create an idol that can only bring death. That may sound "religious" but it's also scientific: how could we ever hear and understand Einstein, or Feyneman, if Newton's words had been written in stone and made unchallengeable by law?