They don't believe it's unconstitutional. They believe it conflicts with the Administrative Procedure Act from 1946. Something that they apparently believe the unanimous decision in Chevron from 1984 got wrong.
I know little about US law, but I thought one of the priciples of common law is that once a precedent is set then it is set forever unless changed by statute? Allowing a court to change precedents undermines the whole concept of common law doesn't it?
This is stare (“starry”) decisis, and while it is absolute vertically, it is less so horizontally. Basically the court can decide that it got it wrong before, but the 9th Circuit is bound by a higher court’s precedents (SCOTUS in this case): https://www.law.cornell.edu/wex/stare_decisis
With the caveat that the appeals courts set lots of precedents where the cases never reach the Supreme Court, in which cases the appeals courts are as bound by their precedents as the SCOTUS is by its precedents (i.e., not really).
Technically, SCOTUS, as the highest court, isn't beholden to anyone's precedent. This year's SCOTUS is just as legitimate as last year's, so they always have the power to overturn past decisions. Lower courts have to follow what higher courts decide, but SCOTUS has no higher authority. And sometimes, like in Brown vs. Board of Ed (which ended legal segregation), it's a very good thing for the Court to overturn its past decisions.
But in practice, to non-lunatics, stare decisis (the legal principle that says not to overturn, or even consider, topics that have already been decided in the past without an extremely good reason) is an incredibly important prior to bring into any discussion. If the court actually uses its power to completely rewrite the rules of how government works on a whim - and let's be clear, that's what this decision does - then there's no way for anyone to ever make a plan. Nothing is stable.
Unfortunately, at least 5/9 of the current Supreme Court are either lunatics or blatantly corrupt. Chevron was decided unanimously for a reason. There is no way to administer a modern state without that concept - which is why right-wing extremists are so happy to see it gone, because they don't want the state administered.
