Allegory as the nature of reality
Chesterton's argument begins with his treatment of human experience. He says that there is an obvious narrative quality of Christianity as a religion (it is a narrative religion in that it is literally a religion built around the "story" of the gospel, for instance, which comes embedded in a long chain of the stories of human lives). That makes the religion applicable to reality, because Chesterton feels that the simultaneous human craving for both chaos and order is a sign that we are fixed in an allegorical reality.
Religion and riddles
Chesterton notices that the sacred feeling one gets about their own life can be expressed in this way: sometimes humans experience religious wisdom as a trustworthy solution to a perplexing, paradoxical set of riddles. Why do humans crave safety and danger? Why do humans crave companionship and independence simultaneously? To get to the bottom of such difficult existential questions requires religion, says Chesterton.
The motif of a secular future
Chesterton does not sympathize with the late modernists and early post-modernists. He writes about the origin of those schools, the writing of Nietzsche, which sparked the modern era of philosophical debate. He feels the ideas in Nietzsche and in similar voices who followed are dangerous, because they seek to undermine important kinds of human knowledge by prioritizing pragmatic reality above the search for a true metaphysic.
The archetypal nature of patience and humility
A person's best self, suggests Chesterton, is the self they attain when they address the important, perplexing questions of life, experience, religion, reality, and death, with a sense of patience and humility, as well as a kind of disciplined resolve to not be hasty or extreme, given the mystic, karmic nature of human life. He explains that these virtues are religious beliefs in action, protecting a person from committing to wrong ideas to hastily.
The motif of sacredness
To say something is sacred is to say it is untouchable. Chesterton elaborates arguments defending Christianity from potential intellectual attack. He uses paradox to show that for every valid criticism of Christianity, there is a perfectly valid paradox that would negate the criticism. This (quite literal) defense mechanism forms a motif of sacredness around Chesterton's beliefs. By appealing to paradox, he is saying, "I understand critical points of view, but the truth is more complicated than it seems." His Orthodoxy is simply that the real existence of such a religion as Christianity makes it automatically sacred, existentially.