It's actually quite simple. I don't totally object to her bizarrely compelling, yet ultimately unworkable philosophies. I can't even hold her terrible prose against her (I'd consider myself lucky to get a book published in my native tongue, much less an adopted one).*
It's the way Rand, much like Stephenie Meyer, cleverly bootstraps her reader into the place of her main character.
The Twilight novels owe a great deal of their runaway success to the fact that anyone reading them can imagine herself (it's almost always "herself") in the shoes of Bella Swan. Who doesn't want to imagine that the reason a hot guy seemingly doesn't like you is because, in fact, he LOVES you? And would do anything for you? Has, in fact, waited his whole immortal life for you? And that despite your ordinariness, everyone is falling all over themselves to befriend and date you?
It's seductive, this vision of self-as-Bella. And as it has made Stephenie Meyer a bazillionaire, I won't throw any shade her way for recognizing that and capitalizing on it.
Which leads me to Ms. Rand.
With novels like The Fountainhead and Atlas Shrugged, you have the EXACT SAME PHENOMENON. Only instead of being able to fantasize about being the It Girl, you get to fantasize that you're the only one who Gets It. Everyone who reads Ayn Rand identifies with Howard Roark, the brilliant (brilliantly brilliant! the brilliantiest!) architect who is Up Against The World. Dagny Taggart and Hank Reardon, capitalists and scientists! They're Unique! They're Special!
Wouldn't you know it -- they're JUST LIKE THE READER!
Much like Twilight asks us to ignore the obvious (that a girl as supposedly mediocre as Bella would not, in fact, attract a guy like Edward, who also doesn't exist -- and that any girl casting herself in Bella's shoes is similarly destined for real-world disappointment), Ayn Rand asks all her readers to pretend that they are the Atlases who might Shrug, overlooking the fact that none of us know anyone like Roark, Taggart, or Reardon in real life, much less resemble them ourselves. Forget about that little detail -- YOU hold the world on your shoulders! Not all these losers and users. You know who John Galt would invite to his oh-so-exclusive retreat? Why you!
Not really, can we all admit?
* The exception to both of these is her novella Anthem, which is quite lovely, in my opinion, and expresses the most coherent, concise vision of Objectivism, which is still kind of nonsense.