Paradoxes and revolution

In Chapter 6 of 'Orthodoxy', Chesterton notes that Christianity 'was attacked on all sides and for contradictory reasons'. Some found it too meek, some too aggressive. Some found its focus on family wrong, some the cloisters. Then Chesterton realizes that there are two kinds of institutions that would fit the description: one with an 'odd shape' and one with 'the right shape'. He concludes that Christianity might be the 'normal thing, the center'. Perhaps, the states, 'Christianity is sane and all its critics are mad - in various ways'.
Christianity, instead of finding the perfect middle between different virtues, seeks to combine them all without blending: there is room for Joan of Arc and for Francis of Assisi. 'The real problem is - can the lion lie down with the lamb and still retain its royal ferocity? That is the problem the Church attempted; that is the miracle she achieved'.
After realizing that the so-called Christian 'paradoxes' exactly mirror the oddities in this world, the argument in chapter seven is about the possibility of improvement. Chesterton notes three sine qua non 's for genuine improvement, all of which ultimately coincide with Christianity.
First and foremost, we need a fixed ideal for any kind of progress. 'The modern young man will never change his environment; for he will always change his mind.' When we change our objective every week, we will never attain it and the old institutions will remain in place.
'Second, it must be composite. It must not (if it is to satisfy our souls) be the mere victory of some one thing swallowing up everything else, love or pride or peace or adventure; it must be a definite picture composed of these elements in their best proportion and relation'. Of course, this implies that there would be an artist.
The third point is that Utopia is fragile. Man will always have to continue to strive for perfection, things will never remain perfect. This, of course, is a result (and an indication) of the Fall.
As a concluding argument, Chesterton shows that Christianity is truly democratic: it is humble enough to try to listen to simple people.
All these arguments in these two chapters are not proofs of Christianity. They merely point out how Christianity coincides with a certain conception of the world (the conception that Chesterton finds reasonable). As explained in chapter one: Chesterton thought of how the world should be, and realized that he discovered Christianity.