Her ideas are based in a particularly stupid and juvenile form of absolutism and - not so much an inability, but a dogged, ideological refusal - to admit shades of grey. She was a sort of neo-fascist dogmatist, and her simplistic, brutalist "philosophy" reflected that. It appeals to the young because the young are, often through little fault of their own, ignorantly idealistic and woefully inexperienced. It appeals to Americans more than any other nation because America is a nation that loves undemanding, inadequately-examined self-mythologising. Outside of the USA people either do not know Rand or else they read her books and marvel at the fact that they remain popular in the US, and even moreso that she's seen as any kind of philosopher or thinker.

This is a good article. It gives some insight into why Rand was the way she was, I think.