>>1704011usfs is arguing that the mineral leasing act grants the ability for agencies to grant right-of-way through federal lands that aren't part of the national park system. however, cowpasture is countering that the appalachian trail is part of the national park system, and the trails act establishing the appalachian trial is more recent than the acts usfs is using.
usfs is then arguing that the definition of trail used in the trails act does not include the immediately surrounding land, effectively just the actual trail itself. cowpasture is countering that by suggesting that the definition of trail that usfs is overly narrow, and pointing out that the government has refered to the appalachian trail area as "land" in plenty of other places. this is the one where the court might lean towards usfs, it's kind of up in the air imo.
finally, usfs makes some weird argument about how congress didn't transfer the trail to the secretary of the interior in the same way that they did in other acts passed at the same time. cowpasture responds that the trails act literally says "The Appalachian Trail shall be administered primarily as a footpath by the Secretary of the Interior", which was meant to be a more specific designation than the general authority the usfs has over national forests.
i haven't fully read the appellate decisions and stuff so this is in no way a complete summary of what's going on here, just brief summaries of what i've picked out from reading a bit about the arguments.