Aside from extended rants from semi-adults stunned to discover that the Chronicles of Narnia can be read as a Christian allegory - as can Harry Potter, The Lord of the Rings (Tolkien himself claimed that the work was fundamentally and consciously Catholic), and most hero narratives of the post-Christian era - and bent on complaining that they have been brainwashed (though apparently not effectively), the major complaint against C. S. Lewis's fantasy series is referred to as the "problem of Susan." Neil Gaiman has written a short story with that title about Susan's post-Narnian life, Philip Pullman has ranted extensively about it, and even the illustrious and usually on-the-ball J. K. Rowling has agreed with the "problem of Susan" theory.
The "problem of Susan" is an argument that attempts to parse out why Susan is the only one of the children who have visited Narnia who does not go to the Narnian heaven at the end of the apocalyptic final novel, The Last Battle. The argument states that Susan is excluded because she has discovered or is exploring her sexuality, based on these sentences - "She's interested in nothing nowadays except nylons and lipstick and invitations. She was always a jolly sight too keen on being grown-up."
First of all, why are we assuming that nylons and lipstick express sexuality? Being grown-up may translate today to being sexual, but we also live in an age in which the coming-of-age story has come to be understood as, ipso facto, a sexual coming-of-age story. This was not always the case. And why emphasize the nylons and lipstick, and ignore the invitations? It is the inclusion of invitations that should invite a different interpretation. Alan Jacobs in his marvelous biography of Lewis, The Narnian, writes, "it is clearly not sexuality that is Susan's problem but rather an excessive regard for social acceptance: she wants to be 'grown-up' because she is at an age when being grown-up is the greatest possible good and being childish the worst possible crime. Susan has been distracted from Narnia not by sexual desire but by the desire to be within the Inner Ring."
The concept of the Inner Ring was fundamental both to Lewis's writing and to his private philosophies. Lewis felt that much of the evil in the world (or, after his conversion, many of the means by which the Devil promulgates evil) was due to a blinding desire to be part of a superior, enclosed elite. This concept came alive for him during his torturous years at public school where strict hierarchies led to flagrant physical and psychological abuse - what today we would consider hazing. Two of the children who visit Narnia, Edmund and Eustace, are both initially corrupted by striving to be in the Inner Ring. This attempt leads them to bully others and selfishly sacrifice those who love them, allowing themselves to be blinded by greed and spite. For Edmund, it takes a revelation of the White Witch's extreme evil and a near assassination, and for Eustace, a painful and agonizing transformation into a dragon, to recognize that it is more important to care for others, selflessly sacrifice oneself, and open one's eyes to the truth than to penetrate the Inner Ring. The evils of this sort of social conformity and snobbishness are also explored in That Hideous Strength, Lewis's great science fiction novel.
It's also worth saying that Lewis had very tolerant views towards the animal passions. Though he was intensely private about his sexual life, even in his diaries,we do know he loved good eating and drinking and felt that the physical pleasures in life were some of God's blessings. He absolutely did not believe in abstinence; he believed in moderation.
Thus, Susan is excluded from Narnia because she has turned her back on it as a childish thing and embraced a quest to join what we might call today the popular crowd. While Peter, Lucy, Edmund, and the others never let go of their belief in Narnia, Susan loses faith and thus could not perceive the joyousness of the afterlife, even if she were there, like the dwarfs who tragically believe themselves to be trapped in a smelly stable because they no longer believe in Aslan.
It's also worth saying that Susan is not necessarily shut out forever. If she regains her faith before her death, she would be brought back to the fold. Remember that in Lewis's conception of the Narnian afterlife, one may cross over to the English afterlife - the Pevensies are told that they can visit with their parents. Susan may rejoin her family and her Narnian friends. But she will have to cease trying to enter the Inner Ring.
Before we go on, I'm not arguing that Lewis wasn't a sexist - he absolutely was, at least while he was writing the Chronicles. I would argue that his views on women changed drastically as a result of his love for and tragically short marriage to Joy Gresham, but that's another subject. There are many examples of sexism in the Chronicles; the one that always bothered me the most is in The Lion, the Witch, and the Wardrobe, when Father Christmas tells Lucy and Susan that they are not to participate in the battle against the White Witch because "battles are ugly when women fight." But sexism is not the same as erotophobia or sexual teetotalism.