You do not own the border.
You own your property: your income, your house, your car.
But the border is not your property. It does not belong to any one person. The border belongs to an aggregate of individuals on both sides of the border who own the land alongside it.
If you are one of those individuals who owns property along the border you have a right to prevent an immigrant from setting foot on your property.
But if an immigrant wants to cross the border to visit me on my property, what right is it of yours to prevent that freedom of movement from taking place.
Certainly, you have a right to keep that immigrant off your property, but you have no right to keep that immigrant off my property.
The country should not have a right to force you to give to it, through taxation or eminent domain, pieces of your property, but neither should you have a right to prevent the travel of an immigrant across property that does not belong to you destined for other property that does not belong to you; temporarily or otherwise.
If I want an immigrant to stay on my property, what right do you have to prevent them from crossing the border.
The country, collectively, isn’t your property anymore than my house or my income, collectively, isn’t your property.
Subsequently, if an immigrant acquires their own property, through income or purchase of land, what right do you have to prevent them from crossing the border across land that does not belong to you destined for property that belongs to them.
You all have an unhealthy relationship with a government that collectively steals property via taxation and eminent domain, and now want to use the government to collectively exert forcefully your will on border adjacent properties that do not belong to you.
This is a problem and not the way to Liberty.