People object to Ayn Rand quotes because they believe her politics to be naive, or her fiction to be heavy-handed. I cannot speak to either of those things one way or the other.

Even giving these things, these are of course no reason to never quote her. Hell, there is a time and a place for quoting even Himmler.

I believe that many left-leaning political types strongly dislike and attempt to discredit Ayn Rand because they vehemently disagree with her political philosophy. A common criticism is that her philosophy sounds good when you are a child, but when you grow up you realize it doesn't work in the real world.

For myself, I'm a 40 year old that leans Libertarian so I tend to agree with some of her political philosophy. I even tried reading Atlas Shrugged but it was so boring I put it down after about 100 pages.

They make some people's head 'splode, others generate kneejerk responses. For an otherwise obscure writer, that that she is so well known to have detractors everywhere is itself telling, but you'd have to judge for yourself what it is telling about.

It's essentially the equivalent of quoting Karl Marx. They are both so blinded by adherence to a since-discredited world view that their positions are laughable at best and at worse provide excuses for destructive behavior. Those who quote either typically haven't bothered to branch out beyond a simplistic, falsifiable perspective. Such an approach supports the smug self-satisfaction of dogmatic certainty over actually being correct.

Or, more succinctly, "There are two novels that can change a bookish fourteen-year old's life: The Lord of the Rings and Atlas Shrugged. One is a childish fantasy that often engenders a lifelong obsession with its unbelievable heroes, leading to an emotionally stunted, socially crippled adulthood, unable to deal with the real world. The other, of course, involves orcs." - John Rogers

There are several problems with Ayn Rand.

One is that her ideas were not particularly original, and not particularly well-expressed. Self-centered philosophies are far from new, and actually are pretty well-trod ground, but her work does little to address already-existing critiques and, as literature, is not particularly good (her characters tend to be one-dimensional, plots lack good development/tension/resolution, etc.).

Another is that she has become a frankly cult-like figure, with people approaching her work the wrong way around: rather than "this statement is correct, and Ayn Rand said it", too often there is a seeming attitude of "this statement is correct because Ayn Rand said it". The Objectivist movement (people who follow her work and philosophy) is particularly infamous for this, having an established history of venerating her and doing some rather extreme turns when she was alive and particular people from her circle fell out of her favor.

Finally, most of her work is easy to critique with only very basic reasoning/argumentative skills, despite presenting itself as a solid, rationally-justified framework. More realistically, Rand's philosophy consists of appeals to emotional responses, based on the idea of self-evaluation of one's own greatness and the notion that this greatness exists more or less in a vacuum (one of the famous examples is "going Galt", wherein all of the great people who produce value simply retreat and form their own separate society, to spite the "parasites" who "leeched" off their work).

To continue with the fiction theme, one of Heinlein's stories ("The Roads Must Roll", 1940) anticipated and harshly criticized the type of philosophy Rand ended up promoting. One of the asides there is to a philosophy of "Functionalism"; the founder of the philosophy advocates evaluating people -- and giving them power and prestige -- based on what "function" they can perform, and how valuable it is to society.

The result is large numbers of people who do not really make any unusually-significant contributions, but who all come to the conclusion that whatever they do is the one truly indispensable thing, and if they stopped doing it the whole society would fall apart, so they should be given more power or prestige over others in recognition. As Heinlein puts it, "With so many different functions actually indispensible, such self-persuasion was easy." Heinlein also offers a description of the founder of "Functionalism" which critiques the philosophy and in many ways critiques Rand's later work as well, when he says:

The complete interdependence of modern economic life seems to have escaped him entirely.

(see Wikipedia for a summary of the story, or look it up -- it's been republished/anthologized: http://en.wikipedia.org/wiki/The_Roads_Must_Roll)