The federal government owns it through purchase or treaty.
It organized territories on land it owns.
It authorized the creation of new states on those lands.
While I think it's high time a lot of this land was put on the market, it is ridiculous to say that US government seized its own land.
Interesting.
http://www.vlrc.org/articles/44.html
Federal Acquisition of Land Within States
By Bill Howell and J.L. (Jim) Tenney
Does the federal government’s purchase of lands within the boundary of a state require the consent of the state legislature? If we are in a sovereign state, the answer is absolutely, yes! As a Constitutional Republic, if our elected representatives are not accountable and do not uphold our state sovereignty and individual liberties, then we are lost.
Although the Enclave Clause of the U.S. Constitution, Article I, section 8, Clause 17, authorizes Congress to purchase, own and control land within the boundary of a state, it is very specific and limiting as to what type of lands the federal government can own and control within a given state. It also leaves no doubt that the state legislature has to relinquish control of those lands. The relevant portion of the Enclave clause reads:
Congress may exercise exclusive legislative “authority over all places purchased by the consent of the legislature of the state in which the same shall be, for the erection of forts, magazines, arsenals, dockyards, and other needful buildings;”
Can any agency of the federal government come into a state and purchase land without state authorization as any other buyer would? Is it a private property right for a property owner to sell to the federal government? A proper reading of the Enclave Clause shows the answer to both of these questions is NO.