Why do I keep needing to point this out? No, it is not a sound analogy to compare “closed borders” with having a fence around your own yard. In fact, it is a profoundly crappy analogy, since the political crooks in DC do not rightfully own every square inch of land between the Atlantic and the Pacific. You have the right to decide what happens on your property. Not your neighbor’s. The gigantic area called “the United States” is not your property, or the politicians’, or the collective’s, or anyone else’s.
What makes the analogy extra crappy is that, if the politicians did have the right to decide who can set foot anywhere in the U.S., it would mean that “your” property is not your property at all. If politicians, and not you, get to decide whether some dude from Mexico is allowed to come visit you, then Congress owns that house, and you don’t. So to pretend that “closed borders” is pro-property-rights or pro-freedom is just ridiculous.