Forget Ayn Rand, ignore Robert Nozick, push aside all the cacophony of recent writing about libertarian ideas. If you want to understand American libertarianism - including the conflicts and contradictions inherent in what it says - go and read Robert Heinlein.
In the early 1970s, according to a survey undertaken at the time by SIL, the Society for Individual Liberty, one libertarian activist in six had been led to libertarianism by reading the novels and short stories of Robert A. Heinlein. Among the prominent libertarians of the late 20th Century who have named Heinlein as an important influence on the development of their own political thinking were Dave Nolan (the founder of the Libertarian Party) and the late Samuel Edward Konkin III.
Here's why maybe?
“I am free, no matter what rules surround me. If I find them tolerable, I tolerate them; if I find them too obnoxious, I break them. I am free because I know that I alone am morally responsible for everything I do.”
Take some time out to read 'Stranger in a Strange Land' or "The Moon is a Harsh Mistress" and understand Heinlein's examination of the contradictions and restrictions of modern America in the former and invocation of the US constitution as the guarantor of freedoms in the latter.
Heinlein's words are echoed in libertarian - and, in America's confused polity - conservatives politics today. Here, from 'Stranger in a Strange Land':
“Government! Three-fourths parasitic and the rest stupid fumbling - oh, Harshaw concluded that man, a social animal, could not avoid government, any more than an individual could escape bondage to his bowels. But simply because an evil was inescapable was no reason to term it "good."
How close this is to Reagan's famous dictum:
The nine most terrifying words in the English language are, 'I'm from the government and I'm here to help.'
I'm sure there are people who prefer to hack their way through the turgid forest of Ayn Rand's prose, to try to empathise with her soul-less, cold characters. But next to the reflections of the author in Heinlein - most of his 'political' works feature an older, wealthy man as the vehicle for that politics - Rand's work lacks impact, few read it without political purpose whereas many will have read 'Friday' or 'Doorway into Summer' just for the good read.
Heinlein doesn't analyse, he merely states those freedoms that Americans cherish- whether or not they profess to be libertarians. None of which makes Heinlein a libertarian although throughout his work, and especially his later work, he always using that knowing quasi-narrator figure as the means to play with political argument and ideas. Whether this is the survivalism (and troubling racial stereotypes) of 'Farnham's Freehold', the war fascism of 'Starship Troopers', the attack on organised religion in 'Stranger in a Strange Land' or the libertarian reworking of the War of Independence that is 'The Moon is a Harsh Mistress'.
In the end Heinlein was a writer who played with ideas, who speculated what they might mean to society, rather than a libertarian polemicist. But his writing always contains that idea of independence, self-reliance and frontier so essential to the American psyche - he doesn't shout or lecture but adopts the stance of the old man sat on the porch dispensing the wisdom of experience and takes his reader with him.
So when people encountered libertarian ideas in Heinlein it was more homespun than the intense, finger-wagging of Ayn Rand or the turgid academia of European writers:
"Must be a yearning deep in human heart to stop other people from doing as they please. Rules, laws — always for other fellow. A murky part of us, something we had before we came down out of trees, and failed to shuck when we stood up. Because not one of those people said: "Please pass this so that I won't be able to do something I know I should stop." Nyet, tovarishchee, was always something they hated to see neighbors doing. Stop them "for their own good" — not because speaker claimed to be harmed by it.”
For all that he was more a contrarian - Heinlein was America's most important libertarian writer. And he liked cats.