The argument seems to be this: “Your house has walls, doesn’t it? Well, then, you must on pain of consistency hold that it’s right to put a wall around the country. If you really believed in open borders, you’d have an open door policy and let anyone come into your house whenever they want.”

Even self-described libertarian websites make arguments like this.

Once again, a nation is not like a house.

Let’s imagine it were. The analogy would prove too much. In my house, I’m free to do all of the following: Forbid almost all people from praying to Jesus. Forbid people from associating with each other, from holding religious services, starting a business, reading LibertyHangout.com, reading the New York Times, starting a club, attending a university, marrying their life-long loves, practicing their hobbies, and whatnot. I can expel almost anyone at any point for any reason, and I can exclude almost anyone I want for almost any reason. You don’t get to exercise your liberal rights in my house.

So, it follows that if our nation is like our house, then we can also forbid people from doing all these things. Just toss out the entire Bill of Rights. After all, you cannot simply exercise your liberal rights in someone else’s house without their express permission, and their permission can generally be revoked at will at any time. Ownership rights in a house give the owners rather strong powers to exclude others and to set terms of association in arbitrary ways.

Instead, a nation is not a single house. It is a collection of houses, of churches, of universities, of open land, etc. It is not collectively owned by all the citizens. (If it were, then, as the paragraph above points out, it follows that liberalism and libertarianism are false.) Rather, individual parts of the nation are owned by different people, while only some parts of it are owned collectively.

When you advocate closed borders, you are not “protecting your or our house”. You are instead advocating that some people use violence and threats of violence to prohibit other people from using their property or associating with others in mutually agreeable ways.