A while since I read it, but it hides it's core ideas in an absurd story that goes on rather too long.

You'll find a consistent set of axioms in most bigger theories. The question is if their model maps well onto the real world (which is fuzzy and inconsistent) or if it needs a lot of "if we only do a little more of X, it might finally work".

My problem with Ayn Rand is that she starts the description of her world view with agreeable statements like "A is A and therefore one can see truth (or draw objective conclusions) just by looking" (which disregards the problem of missing information). But then goes on to draw a moral from that idea which basically negates the whole point of objectivity by making the subject the center of the world. But that's not yet what makes her work propaganda.

What makes her work propaganda is that she, from there "induced" that, since there's only the individual that matters, it is only moral that one tries to maximize one's own happiness and that a fully capitalist society without any regulations whatsoever were we worship the then-to-be-godlike individual entrepreneur would be the only way to achieve said happiness. This also implies that while is is only moral to strive for one's own happiness, there is only a certain kind of individual who actually deserves it. The rest is there to worship or just be screwed over and over again, because there can be only a few winners.

So we've come a long way from making seemingly agreeable statements to justifying a system that dehumanizes most of its subjects (pun not intended) and makes them nothing more but a fleshy mass to the disposal of a select few winners. And that's just what propaganda does: drawing conclusions from a seemingly agreeable standpoint in a way that seems to be logical, but in its essence ignores the fuzziness and incompleteness of the world for the sake of some sense of purity. Don't be fooled by that. There's always complexity hiding somewhere. And while A might seem to be A, you just don't know, how large the hidden b is, yet.

In practice, I'd recommend to look for mental tools that help you analyze but always leave room to deal with the inconsistency of reality. Outside of formal science, consistency is a trap. Building a world view from a set of basic axioms works for mathematics, but not for the extremely complex network that is human relations. I had to learn that the hard way. I'd recommend thinking in networks, path dependencies, path probabilities and network centrality (power) instead. It leads you down a path that allows you to form a much clearer critique than you ever could by adopting Ayn Rand's way of thinking.