I've never understood the analogy. Fences are built to keep people or other animals inside or outside an area, the purpose is almost always fully obvious. They are also not that cheap and require some upkeep, it is almost always easy to find the owner of a fence. I really don't know what sort of fence he had in mind.
The original quote mentions a fence or gate built across a road. Also Chesterton is writing from an English perspective which includes familiarity with manmade landscapes built up over thousands of years where the intentions of the original builders are lost to history. He probably had a dry stone wall in mind which are often used to fence in parcels of land. In any case, I’ll let him defend his position himself, his wit is as sharp as ever:
“In the matter of reforming things, as distinct from deforming them, there is one plain and simple principle; a principle which will probably be called a paradox. There exists in such a case a certain institution or law; let us say, for the sake of simplicity, a fence or gate erected across a road. The more modern type of reformer goes gaily up to it and says, "I don't see the use of this; let us clear it away." To which the more intelligent type of reformer will do well to answer: "If you don't see the use of it, I certainly won't let you clear it away. Go away and think. Then, when you can come back and tell me that you do see the use of it, I may allow you to destroy it."
This paradox rests on the most elementary common sense. The gate or fence did not grow there. It was not set up by somnambulists who built it in their sleep. It is highly improbable that it was put there by escaped lunatics who were for some reason loose in the street. Some person had some reason for thinking it would be a good thing for somebody. And until we know what the reason was, we really cannot judge whether the reason was reasonable. It is extremely probable that we have overlooked some whole aspect of the question, if something set up by human beings like ourselves seems to be entirely meaningless and mysterious. There are reformers who get over this difficulty by assuming that all their fathers were fools; but if that be so, we can only say that folly appears to be a hereditary disease. But the truth is that nobody has any business to destroy a social institution until he has really seen it as an historical institution. If he knows how it arose, and what purposes it was supposed to serve, he may really be able to say that they were bad purposes, that they have since become bad purposes, or that they are purposes which are no longer served. But if he simply stares at the thing as a senseless monstrosity that has somehow sprung up in his path, it is he and not the traditionalist who is suffering from an illusion.”
The sort that controls perfectly spherical cattle?
I also don’t really like the fence analogy. A real fence typically exists to demarcate property lines and / or keep things in / out. This is usually perfectly obvious, even if you don’t know who the owner actually is, or the specific role.