They want a drastic reduction in world population and the survivors to live meek lives of submission under a world government. No more of this free range animals wandering on grazing lands without central management. All their human livestock will go back into the pens where they have been for untold millennia.
Here's the problem. The Neanderthal is the most ironic creature that ever existed in that he has served his brother Jacob for 40,000 years as his servant and yet has never had the character fit for a slave. It is not in his or her nature. There is always something in them that will not submit. There is always something in them that will dream and yearn to simply ignore all this so they can go somewhere to be with their own kind, their animals, their enthusiasms and their accomplishments. You could never breed this out of them. You will never put them at an assembly line and take away their soul. It is not who they are at the molecular level.
Otherwise this would be a simple cattle roundup for melonheads, bringing the beasts back into the stables where they have always been. They want to go. They want to submit. They were never free to begin with, they never had the genes of free peoples. 80% of them are natural born slaves by disposition. The other 20% of the population which represents a spectrum of Neanderthal gene expression are the problematic ones. They will never be proper slaves. If not for them this would be the easiest thing in the world to slam the barn door shut again and close the latch.
Homo Sapiens is a genetically engineered slave class created to kill Neanderthals and to work as laborers on monolithic building projects. He was never designed for independence. He demonstrates every waking second that he is fit to inhabit a hierarchy which will never require him to reason or think for himself beyond simple utilitarianism. It is no accident that people are the way they are. It is by design. You cannot make a mule into a racehorse with shouldas and couldas. The two creatures are incompatible.
This is where I believe the left and the right come from in our society. I think in the r/K ratio it was the Cro-Magnons who were a proligate herd of mindless breeders and the Neanderthals the conservative, quality oriented reflective ones. There's a gigantic gap there and it expresses itself in the huge majority who think it is all about something for nothing and those who want every man to sit beneath his olive tree like Thoreau.
I believe it was the terrible indifference of the Neanderthals to all the great engineering plans and schemes and works of the melonheads that made them hate him for simply not being interested in what he was doing or being a part of it. Have you ever known somebody like that? Somebody who was such a control freak that the worst thing of all you could possibly do was to ignore them? Such people have never gone away. They have always been with us and much of their large brains has been devoted to deception and trickery instead of thinking and problem solving. They have always needed Neanderthals - but Neanderthals have never needed anything but each other. The Neanderthal was a shepherd who dwelt in the high places and went a hundred thousand years requiring nothing but exclusion from everyone else. It seems like everybody always wants to get close to him and live alongside him so they can despise him and take the works of his hands for themselves, being barren creatures with no joy outside of violence and rapine. It seems the Neanderthal had some natural well of goodness that was there in him from the beginning that all the other breeds of men did not have.