Basically, Pullman's series was actually intended as a rewriting of Paradise Lost for teenagers, except that because he is Philip Pullman, he supported Satan's viewpoint throughout the book.
But he has a very, very big flaw.
In Paradise Lost, Milton constantly emphasizes God's omnipotence and role as the creator as arguments for his inherent superiority. Satan's flaw is twofold: he believes himself to be self-created(he argues this because he doesn't specifically remember the act of his creation), and he believes that God's superior power is quantitative, rather than qualitative: he thinks it's a matter of "higher numbers" of power, so to speak, rather than the infinite gap between infinity and any given number. In this, he commits grievous idolatry, by implying that anyone could be equal to God if they simply accumulated enough power, and by failing to acknowledge the inherent distinction between creator and created.
When Pullman argues on the side of Satan, he doesn't merely say he was philosophically justified, but that he was factually correct. Pullman's "God" is not the creator (I could be wrong on this - it's been some time since I've read the books, but I believe he was simply a higher order of angel), and he is most definitely not omnipotent.
So when Pullman rewrites Paradise Lost, his entire argument depends on a completely different set of premises, rather than an actual logical/philosophical dissonance. Because he has to make this change for the arguments espoused in his book to be viable, he completely discredits himself as presenting an actual argument against God's authority.
Putting this in context, consider this quote from the earlier link: "...whereas C. S. Lewis claims that Milton's work succeeds in its stated aim of justifying the ways of God to men, William Empson (Lewis' chief antagonist) has argued that Paradise Lost is good because it makes God look bad. Pullman's position in this debate is unequivocal; he says in his introduction, 'Blake said Milton was a true poet and of the Devil's party without knowing it. I am of the Devil's party and know it.'"
Pullman specifically states that he is supporting the view that God, as presented by Milton, is evil - but he isn't even presenting the same God.
Really, it's just symptomatic of a larger issue: practically every argument against God, be it against his existence or morality, depends on somehow altering his nature. But it's represented especially well here, in the contrast between such prominent works, intrinsically related and yet with very different goals.