This is armed rebellion against the lawful government (which they claim is unlawful) and it is the same attitude that began the Civil War.: "we have a right to whatever we want". Aside from using women and children as human shields, which is a sign of degeneracy and cowardice. At least the Johnny-Rebs didn't do that.
Among the claims made are that the family the gang of thugs showed up to "protect" were subject to illegal "double jeopardy" when their sentence was changed. Double jeopardy applies to someone being acquitted for a crime and then re-tried for the same crime. What happened here was that the trial judge did not impose a mandatory sentence he should have, and an appellate court insisted that the mandatory sentence be applied. Another claim is that the federal government, with the BLM, has "cleared people off of their land" in the west. That did happen when the government moved Native American tribes around, but that's not what these bozos are talking about. What they're talking about is that the federally owned lands administered by the BLM--land that belongs to the whole country--puts some requirements on use by private individuals: if you run cattle on it, you're supposed to pay a fee. This land does not belong to ranchers just because their cattle are on it--they *lease* grazing rights, and the BLM does limit how many cattle they can put there. In return, the BLM does many things to improve the range, to help ranchers deal with predators and competing livestock (such as wild horses and burros), to improve water supplies. Many ranchers get along with his program just fine. Others...think they should be able to use any land that's not privately owned for whatever they want.
The refusal to accept that the government can own land, and manage government owned land for the best interests of the country as a whole, is part of the larger picture of anti-government activism. These people not only want public lands (rangeland, wildlife reserves, etcl) "returned to the people" (by which they mean a small minority of the people--them and their buddies) but they want National Parks, state parks, county and city parks, military bases...everything....returned to private ownership. And they feel that they have personally been harmed by any regulation of their activity on public lands (including damaging them.)
Many ranchers in the west do not own all the land they use. Some lease private lands; many lease public lands. But use does not translate to ownership. If you rent a building, you don't acquire ownership no matter how many years you rent it, or what improvements you put into it. And as knowledge about resource management has grown, the management of federal lands has changed, heading in the direction of sustainability of the resource, and also multi-use sustainability.
So these guys stomp into our national wildlife refuge, take over the buildings and claim they're not going to leave. They're going to convert the refuge to farming. They've already started shooting wildlife, just to prove they can. They've already said they're keeping women and children in the refuge for human shields. And some of their supporters on Twitter are claiming that "the ranchers are the new Indians and the government is the thief, stealing their lands." (The real Indians, by the way, are still there, and would still like the land back from the feds, but the bully boys aren't supporting the Indians...or vice versa, because the Paiutes know that these guys--and those like them--have robbed Indian graves and sold skulls and any artifacts buried with the dead. They're concerned about their sacred sites.) They have shown no interest in or respect for the purpose of the sanctuary and they are in a position to do great, permanent harm, especially since they have been reinforced with fuel and other supplies that can damage the natural water, soil, vegetation and wildlife.
It's clear that they will not leave without violence and are doing their best to position themselves as poor innocent victims of a brutal regime. In situations like this, "patience" and "negotiation" don't work because they're intending to hold out a long time and "negotiation" gives them more time to make act like the victims when really they're the aggressors. In my view it was and is a mistake not to have interdicted access for recruitment, supplies, etc. from day one. It was a huge mistake in Nevada two years ago not to return and handle the Bundy issue firmly and completely. Now we have these people claiming it proves God is on their side that they got away with terroristic threats and theft (they owe the BLM--and us as taxpayers--millions.) It will be a bigger than huge mistake--even if they agree to vacate--to allow them to do so without a complete surrender and fast trip to jail.
[EDITED 1/12/16 to correct misspelling of refuge name.]