Pointing out hypocrisy is not ad hominem, especially when it confirms the point being made. Rand's personal life was marked by a significant rejection of the principles she espoused. Tellingly, the form of her personal rejection takes the form of that "pursuit of pleasure" that Chambers predicted it would take.
Oh, so by trying to 'use' her ideas, that's how you 'realized' that she's a fraud.
No. I attempted to use reason to demonstrate the truth of her assertions (as summarized here, for example). The facts of the real world simply do not permit one to logically reach her conclusions. Instead, one is forced into a long string of assumptions and assertions to justify what she said -- which should never happen with any truly objective system.
Do you have any examples?
Sure. In the link provided, Rand states that:
Man—every man—is an end in himself, not the means to the ends of others. He must exist for his own sake, neither sacrificing himself to others nor sacrificing others to himself. The pursuit of his own rational self-interest and of his own happiness is the highest moral purpose of his life.
There are numerous problems with this. First, of course, "pursuit of happiness" is an utterly subjective concept. It is illogical to base an allegedly "objective" moral philosophy on such a shifty thing. After all, what makes me happy probably differs substantially from what makes you happy. Yet an objective "highest moral good" by definition requires that the same principles apply to everybody -- what makes me happy should also make you happy, all the time.
Next, Rand's contentions about reality and the use of reason (see link), demand that our moral reasoning account for what we observe. Among what we can observe are, specifically, the principles of natural selection, which have been embodied in the Theory of Evolution. Indeed, Rand herself appeals to natural selection when it suits her (e.g., her appeal to laissez-fair capitalism.) I suspect that Rand recognized the potential parallels between "nature, red in tooth and claw," and her own philosphy, which is why she attempted to place constraints on the practices of natural selection. But the world we can observe offers no justification for considering these constraints to be absolutely binding.
Third, an appeal to Evolution suggests that "rational self-interest" can be readily interpreted as "whatever I can get away with." The only thing in Rand's philosophy to prevent that is her assertion that we can't do that. But why not? Unaided Reason -- which Rand raises up as our "only guide to action" -- does not offer an objective answer to that question. At best, one can proffer a limited utilitarian argument that cannot answer the question of what happens when somebody does something they're assured of getting away with.
Fourth, inspection of the real world offers no justification for the assumption that it is a moral imperative for man to "exist for his own sake." Indeed, one could more readily and justifiably invoke the Theory of Evolution to state that man must "exist to further the good of the species." Which of course leads to a philosophy that is radically different from the one Rand lays out.
We could go on in this vein for a long time, but you see where it heads.
You also speak of 'her axioms'. Do you know what the three Objectivist axioms are? (since you're obviously against people speaking on things they don't understand)
The three axioms are discussed here, for example. They actually can be debated, and quite vigorously. (Please note that in what follows I'm merely laying out the argument -- I'm not taking any stand on it one way or the other.) For example, Rand asserted that "Man—every man—is an end in himself." And yet the Law of Identity (a thing is what it is) has some rather obvious flaws when applied to individual humans, especially if they're an "end in themselves". Are you "you" before conception? Are you "you" after you've died? And since most of eternity is made up of times when you're not around, and you're constantly changing when you are around, is it really possible to come to any absolute and logical moral conclusions with respect to you? For example, would it be absolutely wrong for me to hasten your departure from the world, or to prevent your fetus from exiting your mother's womb? It is not at all clear that Objectivism can simply assert the Law of Identity as a basis for a moral philosophy -- there is no logical requirement to accept it as an axiom, and it is a simple fact that there are alternatives to it.
Which do you disagree with?
It is not necessary to agree or disagree with the stated axioms, to recognize that Rand's philosophy does not live up to them. Indeed, the ease by which one can demonstrate that fact, is all the proof necessary to conclude that Ms. Rand was, as I've said, a fraud.
(you've accepted the axioms just by entering a conversation, or even just by existing for that matter)
Nope.
That's interesting. Pope John Paul II teaches the same thing ... that human beings can never be treated as means to any purpose other than their own welfare and sanctification. However, from this premise, Christianity posits an opposite course of action to: He must exist for his own sake, neither sacrificing himself to others nor sacrificing others to himself.
We believe that a person must exist precisely for the purpose of sacrificing himself to the needs of others. Depending on his abilities or circumstances, that will sometimes mean serving others, and sometimes being served, but always dying to self.
The pursuit of his own rational self-interest and of his own happiness is the highest moral purpose of his life.
Christianity teaches that in a world of death, rational self-interest demands that a person love the things of eternity more than the things of time, and that real happiness is found only in loving God and neighbor.
Excellent! I applaud you! You said it much better than I!