The government IS the people, IE it's citizens... immigrants are guests in the nation in the analogy, illegal immigrants broke in through the window in the middle of the night.
It's called an analogy. As a citizen, this nation IS my home.
Strictly speaking, there's nothing in that constitution that says "the president shall not cancel someone's building permit after he's started building" or "the president shall not cancel someone's travel permit after he's started travelling" or anything like that.
"The president shall not cancel anyone's health insurance while they're in an ambulance on the way to hospital". The constitution does not say that either. It doesn't go into that level of detail.
It doesn't even say that when the government issues a permit (a building permit, visa to travel, a driving license, whatever) then the president can't revoke it on a whim.
I think most people would want government to be trustworthy, reliable etc., though. If you get a license to operate a business or permission to return home from a conference, you should be able to rely on having that.
It's called an analogy. As a citizen, this nation IS my home.