A lot of the theory in this book shares the same analytical shape. One might call it a juxtaposition of idealism and realism. Through analysis of the ideal perfection of the various dynamics which are obvious in the real world, a political theory emerges from Arnold's opinion of art. This is rooted in a question of something's theoretical end, meaning the teleological end, as in the phrase, "the means to an end." Arnold's opinion is that the telos of art is the freedom to exist in a sovereign way.
But the reality of the situation is that only a small minority of humans ever do get to be completely sovereign. For instance, one is not able to do whatever one wants to do if the law gets involved. The law is the extension of a governing force that keeps people in a specific order. Arnold sees art as essentially incompatible with government, so that culture becomes a check and balance of its own. Art can inspire social and political movements, so it can be seen as a type of rebellion against power.
This is why teleology is involved. Going to an art show or a local concert or something, one does see aesthetically that there are rebellious personalities in the mix, and true artists often eschew cultural norms entirely. Teleology allows an observer to see what art is "getting at." Arnold's experience of art is that it is an expression not only of one's self, but also of the right to be one's self. This apologetic aspect can be followed to its end. Artists tend to be those who are not inherently obedient and submissive to authority, and the telos of that dynamic is Anarchy.