The most troublesome thing about libertarianism as preached by Ayn Rand is not that the ideology is illogical and irrational. The most annoying thing is that it is anti-human and anti-scientific. It is the mirror image of communism in terms of denying the nature of man.
Human beings belong to a larger family of great apes called ‘Hominidae‘. In this grouping you will find quite a diversity of traits and behaviours. Hominids can be divided into two subgroups: homininae and ponginae. Ponginae contains the Orangutan, and the homininae contain Bonobos, Chimpanzees, Gorillas and humans.
One could say that gorillas, bonobos and chimpanzees are the control group in the study of humans, and it is clear that there are a number of traits which span the whole group. Chief among them is that all homininae form clans and communities. Another thing that the way the homininae form their clans and communities is universal. All communities have a hierarchy with an alpha leader on top, and individuals with lesser status below that.
The idea of individualism as practised by the libertarians is antithetical to the way all the homininae structure their societies, and for this reason the ideology is quite anti-human. Communism wants to rework man to remove the ego; libertarianism wants to rework man to remove the community. Both are as extreme as the other, and both are as anti-human.