The thing that makes you different from the beasts is that you believe that there is a way things ought to be, regardless of how they are. You can view your desire to eat a doughnut separate from your prescriptive belief of whether you ought to eat the donut. You can beliefe that you ought not to eat the donut even though you want to, you can beleive that you ought to eat the donut even if you don't want to. You can even believe that you ought not hold any beliefs regarding what you ought to eat based on your desires to eat it.
Accepting that prescriptive beliefs exists, the claim by Chesterton is quite simply factual. It would be much truer to say that a man will certainly fail, because he believes in himself. Complete self-confidence is not merely a sin; complete self-confidence is a weakness.
The question as to what prescriptive beliefs we ought to hold is another matter, and one Chesterton has dealt with masterfully.
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When I had written this down, I felt once again the presence of something else in the discussion: as a man hears a church bell above the sound of the street. Something seemed to be saying, "My ideal at least is fixed; for it was fixed before the foundations of the world. My vision of perfection assuredly cannot be altered; for it is called Eden. You may alter the place to which you are going; but you cannot alter the place from which you have come. To the orthodox there must always be a case for revolution; for in the hearts of men God has been put under the feet of Satan. In the upper world hell once rebelled against heaven. But in this world heaven is rebelling against hell. For the orthodox there can always be a revolution; for a revolution is a restoration. At any instant you may strike a blow for the perfection which no man has seen since Adam. No unchanging custom, no changing evolution can make the original good any thing but good. Man may have had concubines as long as cows have had horns: still they are not a part of him if they are sinful. Men may have been under oppression ever since fish were under water; still they ought not to be, if oppression is sinful. The chain may seem as natural to the slave, or the paint to the harlot, as does the plume to the bird or the burrow to the fox; still they are not, if they are sinful. I lift my prehistoric legend to defy all your history. Your vision is not merely a fixture: it is a fact." I paused to note the new coincidence of Christianity: but I passed on.