A month ago or so, I was gifted a box set of Ayn Rand's books. I read a couple of them, and have started abhorring her in absolute terms. I can't speak for everyone, but I can say why I dislike her. I find her philosophies childish, selfish and arrogant. Her belief is that the self is the most important thing. A person should be 100% self-serving. This doesn't mean you could volunteer at a charity or the like, but that people should only help others if it makes them feel good.
She also believes that people get what they deserve. If they are strong, have power and money it is because they deserve it. She believes those who have no power or are abused they deserve that for not being strong enough. It is very self-indulgent and egocentric. The truth is that if everyone followed this philosophy the world would be a pretty horrible place. I don't like her idea that the suffering of others should not concern you. Her philosophy is often interpreted as 'Those who have power deserve it, and have no need to share it or lift up the weak and stupid'. Classically, teenagers love the ideas because they are in a phase of discovering their identity and separating from their parents, but the general mood is that her ideas do not lead to happiness or a good society to live in. So people tend to see her fans as using her books to justify their selfishness.
Apart from all of the above, Ayn Rand has always considered herself a moral philosopher first and foremost, and an author and political commentator second. Her philosophy is based on an extreme form of heavily idealised capitalism in which individuals operate only on the basis of their own happiness, and eschew altruism if it would inconvenience them. That last aspect is very important to emphasise - whilst there are capitalists who think self-interest is important for a functioning of a market economy, very few would describe altruism as evil like Ayn Rand did. Here's a quote from her on altruism:
"It is altruism that has corrupted and perverted human benevolence by regarding the giver as an object of immolation, and the receiver as a helplessly miserable object of pity who holds a mortgage on the lives of others—a doctrine which is extremely offensive to both parties, leaving men no choice but the roles of sacrificial victim or moral cannibal."The language is written in extreme, melodramatic and quite graphic terms which is a hallmark of fascist writing. This is something Whittaker Chambers picked up on in a review of Rand's Atlas Shrugged for National Review when he said that the subtext of the book was akin to "Hitler's National Socialism and Stalin's brand of Communism": "To a gas chamber — go!" I personally think that was slightly unfair to Rand - she would have not been in favor of mass extermination of the poor, but I do think there is an element in which her writings dehumanize the most vulnerable in society and ignore their plight. She had a fundamentally simplistic view of capitalism which even the majority of capitalists wouldn't adhere to and as such her entire philosophy is intellectually unsound.
Personally, I remember reading part of Atlas Shrugged a while ago (couldn't finish the thing, I was a 18 year old kid back then) and was surprised at the lengths Rand goes to in order to ignore the arguments she claims to have refuted. I remember reading somewhere a scathing critique she'd written of Rawls' A Theory of Justice, which is probably the most influential piece of political philosophy in the post-war period, and she'd based her entire critique of the book off of a review she'd read of it. To my mind, that's not the approach of someone who's seriously interested in moral philosophy.
Rand also inspired slavish devotion from her followers, and the accounts of her inner circle at the time read more like the workings of a cult than of an ordinary intellectual grouping. Her followers don't just call themselves fans - they call themselves objectivists and base their lives upon a philosophy that tells them they don't need to exhibit kindness towards anybody else and so long as they act as selfishly as possible they're doing the right thing. I think this gets to the other part of your question - many young people (usually men - let's be honest, here) become frustrated with society and turn to Rand's philosophy almost as a piece of intellectual self-help. They usually tend to be first-year university students or slightly younger, and generally grow out of it once they've read a bit further. So it's a point of mockery - the young man proudly waving a copy of The Fountainhead as if he's discovered the key to all life's mysteries - himself.
The point really is not that all accounts of morality or capitalism based on self-interest are intellectually unsound. There's plenty of philosophers like Hayek and Nozick who argued for similar conclusions to Ayn Rand's vis a vis capitalism, but dealt with the issues in a more serious academic sense. Ayn Rand, meanwhile, preferred polemic, battle and above all cultivation of a following. The only reason people really talk about her is because she became something of a phenomenon and her writings have been, popularly speaking, extremely influential.
Also, her philosophical sophistication can be summed up by this story.
At one point the head of her organization started sleeping with her. Both of them were married and this was not some mutually agreed upon open relationship thing. She very publicly flaunted her affair saying it was in line with her philosophy of Objectivism. Despite being married both her and her lover desired to sleep with each other and thus as good objectivists they did. Because who gives a rat's ass about other people's feelings.
Which is literally a core tenet of her philosophy, altruism and selflessness are immoral.
Anyway, this guy start's sleeping with a third woman behind Ayn's back. When Ayn found out she flips and kicks him out of the organization and ostracizes him out of jealousy. And that's Objectivism 101, kids. I can do it because it's my desire and selfishness is good and blah blah blah but you can't do that to me because only my selfishness is good. It's a child's philosophy. It makes perfect sense when you're 15. Which is why those who are older than 15 and publicly identify with her are almost universally:
- High functioning autistics who seem to predominantly make up the fields of engineering and software development and so on
- Psychopaths who, like the above, can't identify the feelings of others, but unlike the above are also incapable of feeling remorse or recognizing others as living beings with rights