Bundy is the modern-day equivalent of the cattle barons who gave the old west the Lincoln County War, the Pleasant Valley War, the Mason County War and the Johnson County Range War.
He wants to graze his cattle on somebody else's land.
The land belonged to the State of Nevada before the Bundy family began to graze their cattle there. Bundy admits that the Bundy family does not own the land. The Bundy family grazed its cattle on the land for free when that was the law, then grazed them while paying a grazing fee when that became the law. When the last grazing agreement expired, Bundy refused to sign a new agreement because he didn't like the terms or the increased grazing fee.
It's no different that if he were grazing his cattle on somebody else's private land.
His family never gained title by prescription or adverse possession. Under common law, adverse possession must be 'hostile,' meaning without permission of the lawful owner. The Bundy family's possession has never been hostile.
Under Nevada law, to gain ownership by adverse possession, a party must gain title under 'color of title,' such as a false deed. The Bundy family has none. Under Nevada law, a person cannot claim adverse possession unless all federal, state, and local taxes on the land have been paid since the time adverse possession began. The Bundys have not been paying taxes on the land since the late 19th century.
Bundy is a thief, trying to steal possession of someone else's land without consent or compensation. He's no different that the cattlemen in the Robert Duvall movie, Open Range.